A - Mixing on the Palette Editorial /

Time Limit: 3 sec / Memory Limit: 1024 MiB

ストーリー

高橋画伯は、新作の水彩画シリーズに取り組んでいる。 彼の作品は繊細な色使いが評価されており、色の調合には特にこだわっている。 あなたは高橋画伯のアシスタントとして、彼が求める色をその場で調合して提供するという重要な役目を担っている。

使用する絵の具は高価であるため、出来るだけ無駄なく色を作ることが求められる。 幸い、これから必要となる色のリストが事前に渡されている。 できるだけ正確に、かつできるだけ少ない無駄でそれらの色を順番通りに作成してほしい。

問題文

絵の具の色は、シアン (C)、マゼンタ (M)、イエロー (Y) からなる三次元ベクトル (C, M, Y) で表される。 ここで、0 \leq C, M, Y \leq 1 である。 色 p_1 = (C_1, M_1, Y_1) の絵の具を v_1 グラム、色 p_2 = (C_2, M_2, Y_2) の絵の具を v_2 グラム混ぜると、色 \frac{v_1 \cdot p_1 + v_2 \cdot p_2}{v_1 + v_2} の絵の具が v_1 + v_2 グラム得られる。

v₁ = 4 p₁ = (1, 0, 0) + v₂ = 6 p₂ = (0, 1, 0) = v₁ + v₂ = 10 p = (0.4, 0.6, 0)

K 種類のチューブ絵の具を所持しており、i 番目のチューブの色は (C^{\mathrm{own}}_i, M^{\mathrm{own}}_i, Y^{\mathrm{own}}_i) である。 各チューブから絵の具を 1 グラム使うごとに、コスト D がかかる。 これらのチューブを用いて、H 種類の色を順番に 1 グラムずつ作成し、画伯に渡したい。 i 番目に作るべき色は (C^{\mathrm{target}}_i, M^{\mathrm{target}}_i, Y^{\mathrm{target}}_i) である。 作成の順番は固定で、変更することはできない。

絵の具を混ぜるパレットは N \times N の格子状のマス目で構成されている。 左上のマスの座標を (0, 0) とし、下方向に i、右方向に j マス進んだ位置の座標を (i, j) とする。

各マスは、上下左右の隣接マスとの間に出し入れ可能な仕切りを備えている。 これらの仕切りの初期状態は、自由に設定してよい。

隣接するマスの間の仕切りが下がっている場合、それらのマスは連結であると呼ぶ。 連結なマス同士をたどって到達可能なマスの集合をウェルと定義する。 仕切りの出し入れによって、複数のウェルを結合したり、1つのウェルを分割して複数にすることができる。

各ウェルには高々1色の絵の具しか入れられず、k マスからなるウェルには最大で k グラムの絵の具を入れることができる。 初期状態ではどのウェルにも絵の具は入っていない。

あなたは以下の操作を、最大で T ターンまで行うことができる：

  1. 任意のマスとチューブを 1 つずつ選び、そのマスが属するウェルに、チューブから 1 グラムの絵の具を出す。ただし、ウェルの残り容量を w とすると、実際に混ざるのは \min(w, 1) グラムであり、残りの 1 - \min(w, 1) グラムは混ざらずに即座に廃棄される。
  2. 任意のマスを選び、そのマスの属するウェルから 1 グラムの絵の具を取り出して画伯に渡す。ただし、そのウェルの絵の具が 1 グラムに満たないようなマスを選択することはできない。
  3. 任意のマスを選び、そのマスの属するウェルから 1 グラムの絵の具を廃棄する。1 グラムに満たない場合は、すべて廃棄される。
  4. 隣接する 2 マス s, t を選び、仕切りを出し入れする。
    • 仕切りを引っ込めたことにより 2 つのウェルが合併された場合、絵の具は混ざって 1 色になる。
    • 仕切りを出したことにより 1 つのウェルが 2 つに分割された場合、容量に比例する形で絵の具も分割される。すなわち、分割前の絵の具量が v、s 側の容量が v_s、t 側の容量が v_t のとき、s 側に残る絵の具量は v \times \frac{v_s}{v_s + v_t}、t 側には v \times \frac{v_t}{v_s + v_t} となる。

操作 2 は、ちょうど H 回行わなければならない。 H 回に満たない、または超過した場合は、WA となる。

計算誤差について

絵の具の量は分数値となるため、操作 2 における「1 グラム以上」の判定を厳密に行うことが難しい。 そのため、ジャッジプログラムでは絵の具量を倍精度浮動小数（double）で管理し、操作 2 の可否判定および取り出し量を、内部値 v（グラム）に基づいて以下のように処理する。

  • 操作可否の判定
    • v < 1 - 10^{-6} の場合：「1 グラム未満」と見なされ、操作 2 は実行できない。
    • v \geq 1 - 10^{-6} の場合：「1 グラム以上」と見なされ、操作 2 を実行できる。
  • 取り出し量の決定
    • v \geq 1 の場合：ちょうど 1 グラムを取り出す。
    • 1 - 10^{-6} \leq v < 1 の場合：ウェル内の絵の具をすべて取り出す。

なお、配布ツールもジャッジプログラムと完全に同一の挙動をするように実装されている。

得点

i 番目に画伯に渡した絵の具の色を (C_i^\mathrm{made}, M_i^\mathrm{made}, Y_i^\mathrm{made}) としたとき、誤差 E を以下で定義する：

\[ E = \sum_{i=0}^{H-1} \sqrt{(C^{\mathrm{target}}_i - C^{\mathrm{made}}_i)^2 + (M^{\mathrm{target}}_i - M^{\mathrm{made}}_i)^2 + (Y^{\mathrm{target}}_i - Y^{\mathrm{made}}_i)^2} \]

操作 1 を行った回数を V としたとき、以下の絶対スコアが得られる：

\[ 1 + D \cdot (V - H) + \mathrm{round}(10^4 \times E) \]

絶対スコアは小さければ小さいほど良い。

各テストケース毎に、\mathrm{round}(10^9\times \frac{全参加者中の最小絶対スコア}{自身の絶対スコア}) の相対評価スコアが得られ、その和が提出の得点となる。

最終順位はコンテスト終了後に実施されるより多くの入力に対するシステムテストにおける得点で決定される。 暫定テスト、システムテストともに、一部のテストケースで不正な出力や制限時間超過をした場合、そのテストケースの相対評価スコアは0点となり、そのテストケースにおいては「全参加者中の最小絶対スコア」の計算から除外される。 システムテストは CE 以外の結 果を得た一番最後の提出に対してのみ行われるため、最終的に提出する解答を間違えないよう注意せよ。

テストケース数

  • 暫定テスト: 50個
  • システムテスト: 2000個、コンテスト終了後に seeds.txt (sha256=e93b5367e87f49c8fe325dbeb0f8daa331d23481c1eb533ff032c7978e39ae04) を公開

相対評価システムについて

暫定テスト、システムテストともに、CE 以外の結果を得た一番最後の提出のみが順位表に反映される。 相対評価スコアの計算に用いられる各テストケース毎の全参加者中の最小絶対スコアの算出においても、順位表に反映されている最終提出のみが用いられる。

順位表に表示されているスコアは相対評価スコアであり、新規提出があるたびに、相対評価スコアが再計算される。 一方、提出一覧から確認出来る各提出のスコアは各テストケース毎の絶対スコアをそのまま足し合わせたものであり、相対評価スコアは表示されない。 最新以外の提出の、現在の順位表における相対評価スコアを知るためには、再提出が必要である。 不正な出力や制限時間超過をした場合、提出一覧から確認出来るスコアは0となるが、順位表には正解したテストケースに対する相対スコアの和が表示されている。

実行時間について

実行時間には多少のブレが生じます。 また、システムテストでは同時に大量の実行を行うため、暫定テストに比べて数%程度実行時間が伸びる現象が確認されています。 そのため、実行時間制限ギリギリの提出がシステムテストでTLEとなる可能性がありま す。 プログラム内で時間を計測して処理を打ち切るか、実行時間に余裕を持たせるようお願いします。

入力

入力は以下の形式で標準入力から与えられる。

N K H T D
C_0^{\mathrm{own}} M_0^{\mathrm{own}} Y_0^{\mathrm{own}}
\vdots
C_{K-1}^{\mathrm{own}} M_{K-1}^{\mathrm{own}} Y_{K-1}^{\mathrm{own}}
C_0^{\mathrm{target}} M_0^{\mathrm{target}} Y_0^{\mathrm{target}}
\vdots
C_{H-1}^{\mathrm{target}} M_{H-1}^{\mathrm{target}} Y_{H-1}^{\mathrm{target}}
  • パレットのサイズ N は、すべてのテストケースで N = 20 に固定されている。
  • チューブ絵の具の種類数 K は、4 \leq K \leq 20 を満たす。
  • 作成すべき色の数 H は、すべてのテストケースで H = 1000 に固定されている。
  • 操作可能な最大ターン数 T は、4000 \leq T \leq 64000 を満たす。
  • チューブから絵の具を 1 グラム出す際のコスト D は、10 \leq D \leq 10000 を満たす。

出力

まず、初期状態における仕切りの配置を、以下の形式で標準出力に出力せよ

v_{0,0} \cdots v_{0,N-2}
\vdots
v_{N-1,0} \cdots v_{N-1,N-2}
h_{0,0} \cdots h_{0,N-1}
\vdots
h_{N-2,0} \cdots h_{N-2,N-1}
  • v_{i,j} は、マス (i, j) とマス (i, j+1) の間の縦の仕切りの状態を表す。v_{i,j} = 0 の場合、仕切りは下がっており、v_{i,j} = 1 の場合、仕切りは出ている。
  • h_{i,j} は、マス (i, j) とマス (i+1, j) の間の横の仕切りの状態を表す。h_{i,j} = 0 の場合、仕切りは下がっており、h_{i,j} = 1 の場合、仕切りは出ている。

次に、最大で T 行の操作を出力せよ。 t 行目には、t ターン目に行う操作を、以下の形式で出力する。

  • マス (i, j) の属するウェルにチューブ k（0 \leq k \leq K-1）から絵の具を 1 グラム追加する場合：
1 i j k
  • マス (i, j) の属するウェルから 1 グラムの絵の具を取り出して画伯に渡す場合：
2 i j
  • マス (i, j) の属するウェルから 1 グラムの絵の具を取り出して廃棄する場合：
3 i j
  • マス (i_1, j_1) とその隣接マス (i_2, j_2) の間の仕切りを出し入れする場合：
4 i_1 j_1 i_2 j_2

例を見る

入力生成方法

  • \mathrm{rand}(L,U): L 以上 U 以下の整数値を一様ランダムに生成する。
  • \mathrm{rand\_double}(L,U): L 以上 U 以下の実数値を一様ランダムに生成する。

N, K, H, T, D の生成

  • N=20
  • K=\mathrm{rand}(4,20)
  • H=1000
  • T=\mathrm{round}(4000\times 2^{\mathrm{rand\_double}(0,4)})
  • D=\mathrm{round}(10^{\mathrm{rand\_double}(1,4)})

チューブ絵の具 (C^{\mathrm{own}}, M^{\mathrm{own}}, Y^{\mathrm{own}}) の生成

各 i に対して、以下のように独立に生成する。

  • C_i^{\mathrm{own}}=\mathrm{rand}(0,10^5)\times 10^{-5}
  • M_i^{\mathrm{own}}=\mathrm{rand}(0,10^5)\times 10^{-5}
  • Y_i^{\mathrm{own}}=\mathrm{rand}(0,10^5)\times 10^{-5}

目標色 (C^{\mathrm{target}}, M^{\mathrm{target}}, Y^{\mathrm{target}}) の生成

各 i に対して、以下の手順で独立に生成する。

  1. K 個の値 x_0, \dots, x_{K-1} を、x_k = -\ln \mathrm{rand\_double}(0, 1) により生成する。ここで \ln は自然対数である。
  2. 正規化：x_k' = x_k \Big/ \sum_{j=0}^{K-1} x_j とする。
  3. 次の式により、目標色の各成分を生成する： \[ C_i^{\mathrm{target}}=\mathrm{round}\left(10^5\times \sum_{k=0}^{K-1}x_k' C_k^\mathrm{own}\right)\times 10^{-5} \] \[ M_i^{\mathrm{target}}=\mathrm{round}\left(10^5\times \sum_{k=0}^{K-1}x_k' M_k^\mathrm{own}\right)\times 10^{-5} \] \[ Y_i^{\mathrm{target}}=\mathrm{round}\left(10^5\times \sum_{k=0}^{K-1}x_k' Y_k^\mathrm{own}\right)\times 10^{-5} \]

ツール(入力ジェネレータ・ビジュアライザ)

コンテスト期間中に、ビジュアライズ結果の共有や、解法・考察に関する言及は禁止されています。ご注意下さい。

入力例 1

20 4 1000 60887 3822
0.18582 0.09589 0.89627
0.52420 0.23682 0.12026
0.25071 0.05604 0.49650
0.65334 0.67404 0.51617
0.44983 0.33494 0.51708
0.46831 0.36471 0.48477
0.50643 0.31952 0.31758
0.34193 0.20682 0.60385
0.44749 0.24562 0.32353
0.38963 0.30694 0.64772
0.41326 0.25529 0.43863
0.48102 0.28265 0.32024
0.52488 0.36664 0.34324
0.37841 0.18944 0.41168
0.29373 0.15923 0.65076
0.35448 0.20560 0.51296
0.32367 0.22647 0.69556
0.47855 0.38877 0.51374
0.31896 0.23366 0.72780
0.49895 0.43287 0.54629
0.50653 0.40515 0.43852
0.36207 0.20372 0.49564
0.43069 0.24221 0.40260
0.23646 0.14069 0.81177
0.33649 0.14485 0.47898
0.29053 0.10922 0.53120
0.41253 0.31572 0.60214
0.47525 0.36316 0.48463
0.29441 0.19318 0.71019
0.39693 0.30065 0.59040
0.47544 0.34956 0.45466
0.57420 0.53898 0.49769
0.36125 0.18511 0.46405
0.28114 0.13901 0.65753
0.42559 0.31318 0.50172
0.31850 0.14022 0.48070
0.43447 0.25413 0.37324
0.27765 0.12952 0.63338
0.42026 0.20582 0.35968
0.40867 0.35087 0.65872
0.46671 0.33422 0.45248
0.51818 0.49577 0.59932
0.38677 0.16434 0.36316
0.41071 0.25720 0.50019
0.38637 0.28906 0.59335
0.38513 0.15798 0.34108
0.33258 0.18452 0.58085
0.44418 0.33675 0.51918
0.49809 0.38033 0.42463
0.48630 0.24091 0.22993
0.33911 0.21807 0.61781
0.42081 0.25516 0.45980
0.51552 0.35164 0.33459
0.46662 0.24812 0.30811
0.31091 0.13384 0.49291
0.36123 0.18389 0.48357
0.42083 0.33545 0.57297
0.24826 0.07514 0.57140
0.48340 0.29052 0.31278
0.41422 0.28879 0.48976
0.34047 0.15474 0.49593
0.42539 0.20087 0.31734
0.61918 0.62082 0.52287
0.53754 0.46574 0.47679
0.31430 0.16010 0.57151
0.49821 0.43923 0.52764
0.37116 0.17485 0.45613
0.41968 0.33169 0.56024
0.40143 0.21709 0.42981
0.45401 0.26611 0.34206
0.25283 0.11414 0.65734
0.43559 0.23650 0.35251
0.28132 0.13919 0.61400
0.44600 0.29304 0.44414
0.29386 0.18632 0.68865
0.37793 0.17775 0.43777
0.53484 0.36935 0.32178
0.32996 0.18432 0.57826
0.45625 0.39205 0.57966
0.51740 0.32952 0.29365
0.52788 0.45634 0.49549
0.33898 0.25731 0.71951
0.44241 0.33788 0.50348
0.35541 0.21045 0.52630
0.28594 0.11714 0.55638
0.38528 0.26185 0.53964
0.36372 0.23391 0.55801
0.42212 0.18381 0.28939
0.39016 0.18518 0.43193
0.21601 0.09441 0.76809
0.27693 0.10150 0.52196
0.30610 0.19654 0.66791
0.60784 0.60530 0.52955
0.38758 0.23651 0.47152
0.47542 0.35640 0.47930
0.26975 0.08320 0.51065
0.30890 0.19992 0.68417
0.34053 0.19379 0.56401
0.36427 0.23960 0.54362
0.51527 0.24233 0.15570
0.23484 0.13811 0.81603
0.46326 0.39133 0.53309
0.42472 0.28718 0.46265
0.30960 0.11880 0.48909
0.49687 0.37474 0.41680
0.48903 0.42773 0.52723
0.44700 0.28841 0.41649
0.35855 0.28369 0.69817
0.49270 0.34811 0.38421
0.30698 0.13072 0.49701
0.27151 0.13131 0.63046
0.40535 0.27205 0.53082
0.37917 0.23776 0.56343
0.32758 0.26528 0.76626
0.28313 0.10240 0.51453
0.47578 0.41780 0.56286
0.32558 0.20836 0.64099
0.44368 0.32861 0.51686
0.31218 0.14542 0.58331
0.37343 0.23308 0.53390
0.45770 0.29193 0.37981
0.31103 0.10728 0.45058
0.40665 0.21431 0.39251
0.25911 0.09397 0.60506
0.24973 0.09796 0.64991
0.45825 0.23037 0.27616
0.45709 0.36803 0.49978
0.43947 0.23210 0.36806
0.49588 0.43143 0.53141
0.37195 0.20703 0.51556
0.33823 0.23018 0.65856
0.32297 0.16941 0.57422
0.51906 0.34404 0.31292
0.52091 0.49850 0.59121
0.49768 0.41697 0.52582
0.64283 0.65561 0.51212
0.47340 0.35644 0.44303
0.32445 0.13570 0.48520
0.37836 0.29651 0.65980
0.44393 0.31058 0.46229
0.51271 0.38156 0.38824
0.41919 0.23616 0.40111
0.31696 0.21470 0.66485
0.36187 0.15793 0.39873
0.33112 0.17579 0.52526
0.50810 0.44279 0.53011
0.27695 0.13854 0.65980
0.34142 0.24699 0.67210
0.54520 0.49387 0.50807
0.37351 0.20697 0.51868
0.40948 0.20573 0.39380
0.30347 0.14252 0.60282
0.45493 0.33104 0.49910
0.46996 0.24048 0.25992
0.44870 0.33279 0.47613
0.35021 0.23599 0.63203
0.35027 0.18268 0.46334
0.46212 0.34810 0.46899
0.42406 0.29380 0.51217
0.51509 0.46435 0.53852
0.52535 0.30579 0.23588
0.32652 0.14091 0.47141
0.37329 0.28438 0.64844
0.50293 0.39101 0.43957
0.41420 0.28635 0.47622
0.52189 0.44849 0.47513
0.32977 0.11673 0.41520
0.47701 0.24186 0.24655
0.32191 0.11880 0.42559
0.27835 0.11951 0.61444
0.42352 0.22608 0.36133
0.39146 0.20249 0.40450
0.42762 0.34071 0.54675
0.38937 0.19475 0.39669
0.32810 0.15300 0.47146
0.55082 0.47131 0.44498
0.42578 0.20351 0.35533
0.49159 0.44219 0.59019
0.38909 0.30081 0.64422
0.48348 0.24487 0.24198
0.40306 0.27642 0.51488
0.43532 0.24172 0.39891
0.44664 0.38503 0.59799
0.31624 0.17174 0.59362
0.45266 0.40047 0.63044
0.46142 0.32470 0.44064
0.25768 0.09812 0.60710
0.56447 0.47483 0.41952
0.27900 0.15570 0.69234
0.44929 0.38730 0.58634
0.39739 0.19709 0.41886
0.31271 0.13828 0.52453
0.33280 0.11516 0.39520
0.51664 0.36835 0.37471
0.44907 0.20730 0.26272
0.28903 0.14444 0.59899
0.30226 0.17091 0.64518
0.44100 0.38878 0.63621
0.48725 0.31881 0.37688
0.41728 0.25152 0.45120
0.49157 0.42372 0.51206
0.45429 0.25314 0.34952
0.36176 0.20208 0.50472
0.39654 0.19107 0.39475
0.51163 0.38623 0.41311
0.23743 0.10223 0.71228
0.45417 0.22332 0.28083
0.51939 0.42846 0.45441
0.43265 0.27130 0.43699
0.34986 0.15479 0.41821
0.48558 0.41771 0.54109
0.51894 0.33403 0.31016
0.26035 0.08810 0.55976
0.30566 0.20613 0.72550
0.41967 0.32143 0.58556
0.42666 0.25912 0.43614
0.45106 0.29885 0.43046
0.35977 0.21322 0.53124
0.34798 0.15889 0.45161
0.33588 0.15424 0.47390
0.38790 0.20571 0.40890
0.46708 0.38213 0.54878
0.39716 0.25314 0.46813
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0.33032 0.14962 0.48830
0.48351 0.43966 0.58452
0.52656 0.39266 0.39054
0.52399 0.39903 0.39315
0.30832 0.16831 0.61605
0.34926 0.27593 0.71484
0.32688 0.16799 0.56803
0.43387 0.34198 0.52984
0.40579 0.28758 0.55714
0.32288 0.18696 0.61787
0.33381 0.16196 0.49977
0.44350 0.25468 0.37761
0.57518 0.53019 0.48673
0.47684 0.37497 0.47059
0.40808 0.25671 0.45082
0.37496 0.16666 0.39693
0.27451 0.17998 0.77362
0.49003 0.39172 0.49270
0.30380 0.13521 0.56491
0.51495 0.32200 0.29475
0.22029 0.11528 0.80875
0.41768 0.36184 0.66118
0.40000 0.18926 0.36812
0.28820 0.19208 0.75692
0.29570 0.13187 0.57044
0.36683 0.27676 0.64787
0.29475 0.13965 0.55533
0.47869 0.44014 0.61303
0.39663 0.21783 0.42759
0.36641 0.27375 0.62813
0.26097 0.08057 0.53886
0.30676 0.23506 0.77758
0.38082 0.20548 0.45518
0.49711 0.37736 0.42425
0.45554 0.38151 0.53854
0.51347 0.32362 0.29327
0.30433 0.21301 0.74267
0.45121 0.23177 0.31139
0.38431 0.21927 0.49987
0.33868 0.14797 0.43176
0.46443 0.34079 0.46791
0.48905 0.41488 0.52346
0.46707 0.38509 0.55971
0.42740 0.33508 0.55888
0.34249 0.22229 0.60318
0.45079 0.34535 0.48882
0.27391 0.13729 0.65909
0.25997 0.16704 0.79268
0.54093 0.48971 0.51260
0.39670 0.23080 0.42615
0.31328 0.21474 0.69215
0.26428 0.16155 0.74977
0.47188 0.40097 0.54011
0.32815 0.15968 0.55008
0.48151 0.24252 0.24964
0.32407 0.21632 0.65625
0.53926 0.29450 0.17749
0.44975 0.19234 0.23278
0.38045 0.29245 0.62159
0.46584 0.38719 0.56459
0.39469 0.21269 0.45712
0.41016 0.22620 0.41422
0.34857 0.27457 0.69958
0.44628 0.28999 0.41277
0.40566 0.27717 0.49184
0.52020 0.42781 0.46396
0.41647 0.33541 0.58805
0.51983 0.46388 0.52052
0.39498 0.29072 0.56436
0.38372 0.30309 0.63455
0.45252 0.30901 0.45849
0.29202 0.19921 0.74297
0.60601 0.55864 0.45038
0.34788 0.16832 0.46465
0.40683 0.27655 0.48944
0.31789 0.23860 0.74934
0.49361 0.40960 0.52242
0.42762 0.18550 0.29616
0.45522 0.39590 0.58503
0.40555 0.19518 0.36071
0.32281 0.18176 0.55807
0.37546 0.23738 0.53053
0.38393 0.17563 0.39200
0.23523 0.09551 0.67909
0.38593 0.17068 0.38818
0.30520 0.17860 0.65689
0.23861 0.13959 0.80865
0.47261 0.41444 0.58368
0.43311 0.27947 0.44061
0.42875 0.33050 0.53334
0.31456 0.16524 0.59703
0.53141 0.36847 0.32234
0.31734 0.15046 0.50310
0.30975 0.15888 0.62019
0.42627 0.33811 0.58103
0.44049 0.35665 0.53961
0.54446 0.52741 0.57951
0.28283 0.14483 0.67559
0.40383 0.30278 0.59587
0.23000 0.07857 0.65997
0.45624 0.31767 0.44944
0.49734 0.44547 0.55942
0.32672 0.15928 0.57012
0.28419 0.17148 0.68652
0.42007 0.31278 0.57313
0.35042 0.18803 0.49661
0.34779 0.20573 0.59199
0.32080 0.22640 0.69593
0.34923 0.21576 0.56005
0.51396 0.43606 0.49591
0.34289 0.23377 0.63080
0.27945 0.10368 0.52394
0.53515 0.44269 0.44326
0.36720 0.19388 0.45437
0.42311 0.31915 0.50790
0.58311 0.52044 0.44438
0.53233 0.40656 0.37888
0.47415 0.36074 0.46755
0.50767 0.25877 0.19787
0.28864 0.16291 0.65309
0.44728 0.33667 0.49650
0.38031 0.27736 0.60965
0.31120 0.14395 0.58810
0.31262 0.18873 0.61311
0.32974 0.16730 0.53356
0.53484 0.49813 0.54488
0.32660 0.15681 0.48723
0.39239 0.27584 0.58787
0.34702 0.14615 0.45219
0.36605 0.17684 0.47815
0.52554 0.39146 0.37580
0.45893 0.23377 0.29367
0.46977 0.40139 0.57336
0.34210 0.21589 0.61972
0.48233 0.38401 0.49703
0.44582 0.35201 0.52477
0.21247 0.09968 0.80361
0.46089 0.38142 0.52047
0.55704 0.39775 0.30522
0.38434 0.23537 0.47198
0.42869 0.37725 0.66028
0.38515 0.19669 0.42578
0.39876 0.22046 0.40558
0.40772 0.21672 0.38397
0.29060 0.20888 0.77131
0.44554 0.35722 0.55759
0.27097 0.13904 0.67219
0.59633 0.54651 0.45178
0.33443 0.22696 0.63088
0.42552 0.32409 0.55249
0.39913 0.31685 0.64002
0.43705 0.19937 0.30907
0.42174 0.32405 0.52952
0.32003 0.18802 0.58206
0.41124 0.19173 0.32615
0.63498 0.64629 0.52028
0.41261 0.28636 0.52187
0.41527 0.19901 0.35073
0.41370 0.37219 0.69585
0.41565 0.34664 0.64131
0.38015 0.29468 0.64257
0.52786 0.45124 0.49182
0.28136 0.14916 0.67420
0.55814 0.46702 0.43073
0.44239 0.30991 0.49368
0.53772 0.50627 0.54902
0.42767 0.29168 0.48154
0.40014 0.26562 0.49595
0.50451 0.33189 0.34337
0.27284 0.11326 0.61226
0.30514 0.14201 0.55821
0.31227 0.16420 0.54576
0.34925 0.28834 0.74368
0.45321 0.28431 0.37489
0.55329 0.51408 0.51386
0.50452 0.45092 0.55650
0.31169 0.16890 0.60175
0.49053 0.22778 0.20586
0.40735 0.35201 0.67687
0.33101 0.17196 0.58589
0.19654 0.09552 0.84831
0.43485 0.32886 0.55654
0.42269 0.28630 0.46251
0.33792 0.26872 0.73404
0.40485 0.33376 0.63209
0.49386 0.33425 0.36824
0.52195 0.35180 0.32021
0.47078 0.42464 0.61150
0.48317 0.40785 0.52743
0.52917 0.46003 0.49586
0.34846 0.21692 0.58468
0.35122 0.18886 0.50916
0.47949 0.42467 0.58903
0.44856 0.34103 0.52612
0.34976 0.23528 0.63677
0.38364 0.21810 0.50030
0.45403 0.34884 0.48296

出力例 1

1 0 1 1 1 1 0 0 0 0 0 1 0 1 1 1 0 0 0
1 1 1 1 1 0 0 0 0 1 0 1 0 0 0 1 1 0 1
0 0 0 1 0 0 1 0 0 1 1 0 1 0 1 0 1 0 0
0 1 0 1 1 0 0 1 1 0 1 0 1 1 0 1 1 0 0
1 1 1 1 1 1 0 0 0 0 1 1 1 0 0 0 0 1 1
1 1 0 0 1 0 0 1 1 1 0 0 0 1 0 0 1 0 0
0 1 0 1 0 1 0 1 0 1 1 1 0 1 1 0 1 0 1
1 1 0 0 1 1 1 0 1 1 0 1 1 1 1 1 1 0 1
0 0 0 0 1 1 0 1 1 0 1 1 0 0 1 1 0 1 1
0 0 0 0 0 0 0 1 1 1 0 1 1 0 0 1 0 0 0
0 1 0 0 1 0 0 1 0 1 0 1 1 0 0 1 1 0 1
0 1 1 0 1 0 1 0 1 0 0 1 1 0 1 0 0 1 1
1 1 1 1 1 0 1 0 1 1 0 0 1 0 1 1 1 0 0
0 1 0 1 0 1 1 0 0 1 1 1 1 1 0 1 0 0 1
1 1 0 1 0 0 0 0 1 1 1 1 1 1 0 0 1 1 1
0 0 1 0 1 1 1 1 0 1 1 1 0 1 0 0 0 1 1
0 0 1 1 0 1 0 0 0 1 1 0 0 0 0 1 0 0 0
1 0 0 0 1 1 0 1 0 1 1 0 1 0 1 1 0 0 1
0 0 0 0 0 0 1 1 0 0 0 1 1 1 1 1 0 1 1
0 0 0 0 1 0 1 1 1 1 0 1 0 1 1 0 0 1 0
1 0 1 0 0 1 1 1 0 0 1 1 0 1 0 1 0 0 1 1
1 1 0 1 0 0 0 1 0 1 0 1 1 1 1 1 0 1 0 0
1 1 1 0 1 0 0 0 0 0 1 0 0 0 0 1 0 1 0 0
0 0 1 1 1 0 1 0 0 1 1 1 1 0 1 1 1 1 0 1
0 0 0 0 1 1 1 0 1 1 0 0 0 1 1 0 1 1 1 1
1 0 1 1 1 0 0 0 0 0 0 1 1 0 1 0 1 1 1 0
0 1 0 0 1 0 1 1 1 0 0 0 0 1 0 0 0 1 0 1
0 0 0 0 0 0 0 1 1 1 1 1 0 1 0 0 1 1 1 0
1 1 1 0 0 1 1 1 1 1 0 1 1 1 1 0 0 1 1 1
0 1 0 1 1 1 0 1 0 0 1 0 1 0 1 1 1 1 0 0
0 1 0 0 1 0 0 0 1 1 1 0 0 0 0 1 1 0 1 0
0 0 1 0 0 0 1 1 0 0 1 1 0 0 1 0 0 1 1 0
0 1 0 0 0 1 1 0 1 1 0 0 0 0 0 1 1 1 1 1
1 1 0 1 0 0 1 0 1 1 1 1 1 1 1 0 0 1 0 0
0 0 0 0 1 1 0 0 1 0 1 1 1 0 0 0 1 0 0 0
0 1 1 1 1 0 0 1 1 0 0 1 0 1 0 0 1 1 1 1
1 1 0 1 0 1 0 1 1 0 0 1 1 0 1 1 1 1 0 0
1 1 0 1 0 0 0 0 1 1 0 1 0 0 1 0 0 0 0 0
0 1 1 1 1 0 0 0 1 1 0 1 1 1 1 0 0 1 1 0
1 5 18 2
4 13 3 14 3
1 19 2 1
2 19 2
1 1 19 3
4 12 1 13 1
1 10 10 2
2 10 10
1 17 9 2
4 15 10 16 10
1 14 2 0
2 14 2
1 8 7 3
4 15 16 15 17
1 3 9 0
2 3 9
1 10 0 3
4 2 8 3 8
1 18 12 1
2 18 12
1 4 4 3
4 2 4 2 5
1 18 5 0
2 18 5
1 5 10 3
4 5 3 5 4
1 13 1 1
2 13 1
1 1 11 0
4 16 8 17 8
1 5 16 3
2 5 16
1 10 0 1
4 12 10 13 10
1 8 3 1
2 8 3
1 0 9 3
4 14 9 15 9
1 7 5 1
2 7 5
1 11 10 3
4 14 11 15 11
1 14 13 3
2 14 13
1 12 10 0
4 9 12 9 13
1 12 18 1
2 12 18
1 2 17 0
4 19 18 19 19
1 9 9 0
2 9 9
1 7 13 2
4 11 6 11 7
1 12 2 0
2 12 2
1 0 12 2
4 14 4 15 4
1 19 8 3
2 19 8
1 9 15 2
4 4 15 5 15
1 14 3 0
2 14 3
1 0 19 2
4 19 4 19 5
1 8 8 2
2 8 8
1 0 12 0
4 14 6 14 7
1 0 7 1
2 0 7
1 17 12 1
4 14 16 15 16
1 6 11 1
2 6 11
1 3 5 0
4 16 19 17 19
1 0 12 0
2 0 12
1 9 8 1
4 10 13 11 13
1 10 2 2
2 10 2
1 15 2 0
4 0 0 1 0
1 11 16 3
2 11 16
1 2 11 3
4 5 5 6 5
1 7 1 0
2 7 1
1 15 4 3
4 17 7 17 8
1 15 8 3
2 15 8
1 7 18 1
4 4 3 4 4
1 5 10 3
2 5 10
1 17 15 3
4 3 17 3 18
1 10 9 0
2 10 9
1 4 5 2
4 0 11 1 11
1 11 9 3
2 11 9
1 5 16 2
4 7 17 8 17
1 8 3 1
2 8 3
1 14 13 2
4 8 12 9 12
1 8 1 0
2 8 1
1 10 10 3
4 2 7 2 8
1 7 5 3
2 7 5
1 0 4 2
4 12 1 13 1
1 6 11 1
2 6 11
1 6 12 2
4 13 5 14 5
1 8 0 2
2 8 0
1 17 13 1
4 4 0 4 1
1 17 5 1
2 17 5
1 10 0 3
4 13 14 13 15
1 8 9 3
2 8 9
1 1 18 3
4 5 10 6 10
1 4 18 1
2 4 18
1 13 2 2
4 5 16 5 17
1 2 6 2
2 2 6
1 18 9 1
4 4 4 5 4
1 4 19 3
2 4 19
1 8 13 1
4 3 6 4 6
1 5 10 2
2 5 10
1 4 2 2
4 4 11 5 11
1 18 15 0
2 18 15
1 15 9 0
4 8 18 9 18
1 13 19 2
2 13 19
1 18 8 3
4 15 4 15 5
1 5 6 3
2 5 6
1 15 2 1
4 10 4 10 5
1 18 13 1
2 18 13
1 14 15 1
4 0 16 1 16
1 8 9 0
2 8 9
1 15 0 2
4 9 16 9 17
1 9 18 1
2 9 18
1 8 5 1
4 1 3 2 3
1 16 1 0
2 16 1
1 18 18 2
4 17 2 17 3
1 1 2 1
2 1 2
1 16 10 2
4 6 6 7 6
1 12 13 0
2 12 13
1 9 17 1
4 11 3 11 4
1 8 7 2
2 8 7
1 15 3 0
4 8 10 8 11
1 0 5 2
2 0 5
1 5 19 3
4 0 18 1 18
1 8 6 3
2 8 6
1 11 16 0
4 10 13 11 13
1 14 15 3
2 14 15
1 16 16 2
4 16 17 16 18
1 6 7 0
2 6 7
1 8 10 1
4 4 18 5 18
1 8 15 0
2 8 15
1 15 12 1
4 3 17 3 18
1 4 4 1
2 4 4
1 18 11 1
4 3 4 3 5
1 1 14 3
2 1 14
1 12 8 2
4 18 3 18 4
1 7 1 2
2 7 1
1 17 10 2
4 5 14 5 15
1 5 16 1
2 5 16
1 4 12 2
4 12 0 13 0
1 18 18 2
2 18 18
1 1 8 2
4 4 1 4 2
1 5 14 2
2 5 14
1 9 9 3
4 18 13 18 14
1 5 15 1
2 5 15
1 11 4 2
4 3 1 3 2
1 8 17 2
2 8 17
1 3 2 2
4 10 15 11 15
1 3 18 2
2 3 18
1 10 4 0
4 10 12 11 12
1 11 14 3
2 11 14
1 11 12 3
4 9 6 10 6
1 17 10 2
2 17 10
1 3 12 3
4 13 16 13 17
1 9 6 3
2 9 6
1 0 5 1
4 6 8 6 9
1 6 2 0
2 6 2
1 1 6 1
4 13 4 13 5
1 13 11 0
2 13 11
1 7 1 0
4 10 18 11 18
1 4 2 3
2 4 2
1 8 11 1
4 12 15 12 16
1 6 17 1
2 6 17
1 8 15 2
4 9 6 9 7
1 19 2 1
2 19 2
1 19 2 0
4 2 11 2 12
1 4 4 1
2 4 4
1 16 0 0
4 9 12 10 12
1 4 17 3
2 4 17
1 18 3 3
4 13 1 13 2
1 13 13 0
2 13 13
1 12 7 2
4 7 11 8 11
1 11 4 0
2 11 4
1 17 12 0
4 1 10 2 10
1 11 3 0
2 11 3
1 12 0 1
4 7 5 7 6
1 4 5 0
2 4 5
1 17 7 3
4 8 9 8 10
1 0 6 2
2 0 6
1 7 12 3
4 0 0 0 1
1 11 17 3
2 11 17
1 17 16 1
4 5 12 6 12
1 5 0 1
2 5 0
1 11 0 2
4 5 15 5 16
1 11 4 3
2 11 4
1 6 14 3
4 18 8 19 8
1 3 7 0
2 3 7
1 15 5 2
4 13 19 14 19
1 12 19 0
2 12 19
1 3 16 1
4 13 11 13 12
1 16 4 2
2 16 4
1 15 4 3
4 14 17 14 18
1 4 14 1
2 4 14
1 2 2 1
4 2 7 3 7
1 7 9 0
2 7 9
1 19 3 1
4 4 15 4 16
1 10 14 2
2 10 14
1 10 19 2
4 10 15 11 15
1 8 12 0
2 8 12
1 12 0 3
4 13 16 14 16
1 7 16 1
2 7 16
1 8 4 1
4 15 3 16 3
1 13 18 3
2 13 18
1 19 19 2
4 6 8 7 8
1 12 17 3
2 12 17
1 15 13 3
4 11 9 12 9
1 18 17 2
2 18 17
1 19 12 0
4 13 12 14 12
1 2 1 2
2 2 1
1 9 18 0
4 0 1 1 1
1 9 8 1
2 9 8
1 0 10 2
4 8 16 8 17
1 12 13 2
2 12 13
1 6 14 0
4 15 11 15 12
1 13 4 1
2 13 4
1 4 15 0
4 14 14 14 15
1 16 18 0
2 16 18
1 5 2 3
4 2 19 3 19
1 11 0 0
2 11 0
1 3 7 0
4 15 4 15 5
1 12 15 0
2 12 15
1 9 12 2
4 0 3 1 3
1 17 16 1
2 17 16
1 12 19 3
4 8 0 9 0
1 18 16 2
2 18 16
1 14 1 0
4 15 13 15 14
1 11 4 0
2 11 4
1 11 5 0
4 18 2 18 3
1 13 12 0
2 13 12
1 3 6 2
4 3 15 3 16
1 1 6 1
2 1 6
1 3 18 3
4 9 0 10 0
1 14 13 2
2 14 13
1 3 1 2
4 10 12 11 12
1 12 12 1
2 12 12
1 9 17 1
4 18 7 18 8
1 16 18 0
2 16 18
1 12 8 2
4 14 17 14 18
1 7 15 2
2 7 15
1 8 18 3
4 6 3 6 4
1 5 13 0
2 5 13
1 16 1 2
4 4 9 4 10
1 16 8 2
2 16 8
1 5 12 1
4 15 3 16 3
1 8 9 2
2 8 9
1 8 4 1
4 18 6 19 6
1 12 2 0
2 12 2
1 6 2 1
4 6 8 7 8
1 3 9 0
2 3 9
1 18 19 3
4 6 1 7 1
1 13 7 2
2 13 7
1 0 14 3
4 12 13 13 13
1 5 18 3
2 5 18
1 14 9 3
4 18 9 19 9
1 6 6 3
2 6 6
1 5 4 3
4 0 6 0 7
1 14 16 2
2 14 16
1 0 5 1
4 9 15 10 15
1 0 7 0
2 0 7
1 3 4 2
4 14 17 15 17
1 9 17 3
2 9 17
1 0 4 3
4 10 17 10 18
1 10 12 3
2 10 12
1 1 12 0
4 1 17 2 17
1 14 17 0
2 14 17
1 8 14 1
4 15 8 16 8
1 17 19 0
2 17 19
1 1 2 1
4 4 6 4 7
1 5 2 2
2 5 2
1 12 7 2
4 15 11 15 12
1 3 16 3
2 3 16
1 16 15 1
4 15 15 16 15
1 17 16 2
2 17 16
1 8 14 0
4 5 3 6 3
1 8 13 0
2 8 13
1 11 1 0
4 15 15 15 16
1 14 6 3
2 14 6
1 2 9 1
4 9 11 9 12
1 13 13 0
2 13 13
1 16 19 0
4 18 18 18 19
1 7 16 1
2 7 16
1 7 9 1
4 11 9 12 9
1 3 8 2
2 3 8
1 2 16 3
4 14 16 15 16
1 13 13 3
2 13 13
1 11 14 2
4 12 10 12 11
1 4 2 0
2 4 2
1 1 4 2
4 6 1 6 2
1 15 0 3
2 15 0
1 1 15 0
4 16 11 17 11
1 5 5 2
2 5 5
1 5 2 3
4 4 11 4 12
1 2 9 1
2 2 9
1 2 12 2
4 4 11 5 11
1 12 19 3
2 12 19
1 17 11 2
4 17 17 18 17
1 15 10 2
2 15 10
1 10 13 1
4 9 14 10 14
1 18 15 0
2 18 15
1 14 14 0
4 12 2 12 3
1 8 18 3
2 8 18
1 16 14 0
4 3 1 3 2
1 4 3 1
2 4 3
1 15 18 3
4 6 4 7 4
1 8 16 3
2 8 16
1 7 16 2
4 16 3 17 3
1 15 6 2
2 15 6
1 15 5 2
4 15 11 15 12
1 6 14 2
2 6 14
1 5 15 1
4 14 8 15 8
1 8 19 3
2 8 19
1 8 14 2
4 15 5 15 6
1 14 1 2
2 14 1
1 18 17 2
4 0 17 1 17
1 2 15 1
2 2 15
1 6 15 0
4 12 11 13 11
1 13 11 2
2 13 11
1 8 5 2
4 2 6 3 6
1 15 12 2
2 15 12
1 13 3 0
4 11 0 11 1
1 1 0 3
2 1 0
1 14 6 2
4 5 13 5 14
1 4 8 2
2 4 8
1 1 14 0
4 15 7 16 7
1 8 14 1
2 8 14
1 0 0 2
4 3 7 3 8
1 2 11 2
2 2 11
1 18 5 3
4 12 6 12 7
1 10 6 1
2 10 6
1 0 12 3
4 17 3 17 4
1 10 12 0
2 10 12
1 19 9 0
4 13 7 13 8
1 5 16 0
2 5 16
1 9 0 0
4 6 2 7 2
1 18 0 0
2 18 0
1 1 9 2
4 12 1 13 1
1 15 17 2
2 15 17
1 7 4 3
4 9 16 9 17
1 10 11 1
2 10 11
1 12 12 3
4 4 10 5 10
1 8 19 2
2 8 19
1 9 14 2
4 16 19 17 19
1 2 9 0
2 2 9
1 13 12 3
4 16 2 16 3
1 12 2 1
2 12 2
1 16 18 1
4 13 8 13 9
1 0 6 2
2 0 6
1 12 7 0
4 6 18 6 19
1 2 1 2
2 2 1
1 3 3 3
4 9 8 9 9
1 5 4 3
2 5 4
1 9 14 1
4 18 9 19 9
1 9 1 3
2 9 1
1 11 2 0
4 8 4 9 4
1 0 12 1
2 0 12
1 4 6 0
4 19 13 19 14
1 8 5 2
2 8 5
1 14 11 2
4 13 8 13 9
1 0 15 2
2 0 15
1 17 5 1
4 18 15 18 16
1 12 14 2
2 12 14
1 17 16 0
4 2 15 2 16
1 15 14 2
2 15 14
1 6 6 0
4 10 19 11 19
1 18 9 2
2 18 9
1 5 3 1
4 18 4 19 4
1 12 1 2
2 12 1
1 15 17 0
4 14 7 15 7
1 7 18 3
2 7 18
1 9 4 1
4 10 9 11 9
1 0 15 0
2 0 15
1 17 16 1
4 9 7 9 8
1 11 15 3
2 11 15
1 4 6 0
4 9 7 9 8
1 17 3 1
2 17 3
1 2 4 0
4 3 4 4 4
1 5 6 0
2 5 6
1 14 10 3
4 19 0 19 1
1 8 15 2
2 8 15
1 4 15 3
4 14 17 14 18
1 3 13 3
2 3 13
1 9 1 1
4 12 7 12 8
1 0 11 0
2 0 11
1 16 12 2
4 18 0 19 0
1 4 10 0
2 4 10
1 9 13 3
4 1 2 1 3
1 6 2 0
2 6 2
1 12 2 2
4 17 3 18 3
1 15 15 0
2 15 15
1 13 4 3
4 18 0 19 0
1 7 17 3
2 7 17
1 3 11 2
4 18 7 18 8
1 0 3 3
2 0 3
1 18 0 0
4 11 10 11 11
1 8 8 1
2 8 8
1 13 16 2
4 9 2 9 3
1 9 6 0
2 9 6
1 18 6 0
4 6 9 6 10
1 8 17 3
2 8 17
1 8 13 2
4 12 3 12 4
1 10 5 1
2 10 5
1 5 19 0
4 3 15 3 16
1 4 15 3
2 4 15
1 7 11 0
4 10 1 10 2
1 19 0 3
2 19 0
1 12 17 3
4 12 7 13 7
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1 16 11 1
4 1 16 2 16
1 5 0 2
2 5 0
1 2 18 0
4 6 16 7 16
1 3 8 2
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1 8 9 2
4 1 11 2 11
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2 11 17
1 15 3 3
4 18 2 19 2
1 18 17 2
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1 10 17 3
4 15 1 16 1
1 11 4 1
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1 9 9 2
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1 2 10 1
4 18 6 18 7
1 1 2 1
2 1 2
1 3 8 2
4 12 16 12 17
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1 16 5 1
4 1 13 2 13
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1 5 13 3
4 2 1 2 2
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4 2 4 3 4
1 12 14 3
2 12 14
1 6 3 1
4 2 18 3 18
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1 14 14 3
4 5 2 5 3
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2 11 16
1 0 14 2
4 2 4 2 5
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2 2 16
1 8 15 0
4 4 15 4 16
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4 4 0 5 0
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4 3 5 3 6
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4 0 18 0 19
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4 4 17 5 17
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4 10 1 11 1
1 0 11 1
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1 8 7 0
4 5 9 5 10
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4 5 19 6 19
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4 8 5 8 6
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4 6 13 6 14
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1 5 2 0
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4 3 6 4 6
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4 14 11 14 12
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2 7 6
1 7 7 2
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4 1 0 2 0
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4 8 17 9 17
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1 2 11 1
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1 3 10 0
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1 1 1 0
2 1 1
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1 12 16 0
2 12 16
1 10 15 3
4 1 0 1 1
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1 8 8 1
4 17 1 18 1
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1 1 4 1
4 18 17 19 17
1 9 5 1
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1 9 17 1
4 16 6 17 6
1 4 8 1
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1 15 3 2
4 3 19 4 19
1 17 8 0
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4 11 8 12 8
1 17 10 3
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1 11 14 3
4 4 1 4 2
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1 7 17 0
4 6 16 7 16
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1 16 19 3
4 2 6 3 6
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1 5 12 1
4 3 18 4 18
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4 15 4 15 5
1 4 7 3
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1 18 3 3
4 2 3 3 3
1 17 16 0
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4 0 3 1 3
1 1 1 3
2 1 1
1 3 12 0
4 13 16 13 17
1 11 16 1
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1 5 2 1
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4 7 4 8 4
1 2 18 1
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4 19 11 19 12
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4 0 18 1 18
1 7 2 2
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1 0 9 3
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1 14 14 2
4 8 17 9 17
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1 6 6 1
4 5 18 5 19
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1 16 5 3
4 7 7 7 8
1 12 16 1
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1 9 17 2
4 3 8 4 8
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2 17 2
1 17 0 2
4 14 12 14 13
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1 12 9 2
4 3 4 4 4
1 12 1 1
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1 10 7 3
4 1 19 2 19
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1 9 9 3
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4 13 19 14 19
1 14 19 3
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4 2 6 2 7
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4 13 1 14 1
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1 8 6 3
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4 14 4 14 5
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4 16 14 16 15
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1 9 0 3
4 13 15 13 16
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4 9 12 9 13
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1 8 4 3
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4 14 14 15 14
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4 13 0 13 1
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4 9 10 9 11
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4 0 9 1 9
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4 16 1 17 1
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4 10 6 10 7
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1 2 9 3
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4 11 1 12 1
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4 12 12 13 12
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1 9 5 3
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1 13 13 1
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1 12 9 1
4 14 13 14 14
1 2 10 1
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4 16 9 16 10
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4 6 11 7 11
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1 14 9 1
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1 7 11 1
4 1 18 2 18
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4 11 13 12 13
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1 5 4 1
4 5 8 5 9
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1 10 14 0
4 18 7 18 8
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4 1 17 2 17
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1 9 16 3
4 12 8 12 9
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1 2 11 3
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1 11 4 0
4 4 0 5 0
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4 9 16 10 16
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4 2 4 2 5
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4 18 9 19 9
1 8 1 1
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4 3 0 3 1
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4 8 15 8 16
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4 11 18 11 19
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1 6 6 3
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4 10 11 10 12
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4 7 13 7 14
1 10 2 1
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4 1 12 2 12
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4 0 5 0 6
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4 9 8 10 8
1 15 1 0
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1 11 16 3
4 4 14 4 15
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4 15 18 15 19
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4 2 1 3 1
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1 6 16 0
4 1 5 1 6
1 13 14 1
2 13 14
1 3 8 1
4 3 12 3 13
1 10 6 1
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1 13 10 3
4 0 15 1 15
1 0 19 1
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1 18 6 3
4 1 1 2 1
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2 4 15
1 15 0 1
4 13 14 14 14
1 6 19 2
2 6 19
1 19 5 2
4 9 16 10 16
1 2 17 3
2 2 17
1 18 14 1
4 3 17 4 17
1 19 1 1
2 19 1
1 13 14 1
4 6 3 7 3
1 17 3 3
2 17 3
1 3 3 1
4 14 18 15 18
1 13 3 2
2 13 3
1 9 9 1
4 17 7 18 7
1 13 14 2
2 13 14
1 12 12 1
4 2 16 2 17
1 9 10 1
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1 8 2 1
4 18 12 18 13
1 4 1 3
2 4 1
1 5 5 2
4 6 14 6 15
1 3 2 1
2 3 2
1 0 6 2
4 7 14 8 14
1 1 2 2
2 1 2
1 14 17 2
4 3 19 4 19
1 4 0 1
2 4 0
1 12 19 3
4 5 19 6 19
1 18 17 3
2 18 17
1 10 6 1
4 0 8 1 8
1 12 6 3
2 12 6
1 0 7 1
4 18 17 18 18
1 5 5 1
2 5 5
1 2 11 1
4 10 10 11 10
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1 17 17 2
4 12 7 12 8
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2 4 18
1 6 10 2
4 15 5 15 6
1 2 16 0
2 2 16
1 19 3 1
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1 13 15 3
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1 12 5 1
4 11 17 12 17
1 16 17 3
2 16 17
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4 4 9 5 9
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1 2 11 0
4 10 11 11 11
1 0 1 1
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1 11 11 0
4 0 8 1 8
1 18 5 1
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1 0 13 2
4 3 10 4 10
1 11 0 3
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1 9 3 0
4 7 3 8 3
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2 9 8
1 14 11 1
4 11 11 12 11
1 16 18 1
2 16 18
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4 14 16 14 17
1 15 17 3
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1 5 8 2
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2 7 13
1 12 19 1
4 18 17 18 18
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4 15 16 16 16
1 2 19 2
2 2 19
1 16 11 2
4 17 3 17 4
1 5 1 2
2 5 1
1 15 14 2
4 13 16 13 17
1 12 12 2
2 12 12
1 3 10 0
4 0 12 1 12
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2 12 17
1 12 6 3
4 12 17 12 18
1 16 8 2
2 16 8
1 5 11 1
4 13 9 14 9
1 7 13 2
2 7 13
1 4 3 2
4 8 16 9 16
1 2 6 1
2 2 6
1 16 16 0
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4 11 9 11 10
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4 15 18 16 18
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1 16 10 0
4 18 7 18 8
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4 16 1 17 1
1 1 13 3
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1 7 18 2
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1 12 14 1
2 12 14
1 19 11 1
4 17 12 18 12
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1 8 11 3
4 14 7 14 8
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4 4 1 5 1
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4 8 9 9 9
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4 8 9 9 9
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4 10 6 11 6
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1 1 6 3
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1 6 11 2
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2 3 8
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4 16 13 16 14
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4 4 12 5 12
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4 11 5 12 5
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4 0 19 1 19
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1 15 19 0
2 15 19
1 3 6 0
4 13 3 14 3
1 13 14 2
2 13 14
1 13 16 1
4 6 16 7 16
1 14 17 1
2 14 17
1 18 13 3
4 16 7 16 8
1 0 19 2
2 0 19
1 8 1 0
4 5 8 6 8
1 12 9 2
2 12 9
1 5 13 3
4 13 10 13 11
1 14 18 2
2 14 18
1 3 6 3
4 18 3 19 3
1 10 3 1
2 10 3
1 3 17 1
4 11 2 12 2
1 2 16 1
2 2 16
1 16 8 3
4 13 11 14 11
1 19 1 1
2 19 1
1 0 5 2
4 1 18 1 19
1 9 4 3
2 9 4
1 17 9 1
4 0 9 1 9
1 11 13 3
2 11 13
1 11 17 1
4 9 15 10 15
1 1 16 0
2 1 16
1 8 14 2
4 4 14 4 15
1 2 10 1
2 2 10
1 19 6 2
4 2 8 2 9
1 14 12 0
2 14 12
1 7 8 3
4 0 15 1 15
1 9 17 2
2 9 17
1 8 2 2
4 7 7 7 8
1 11 16 0
2 11 16
1 18 12 3
4 17 1 17 2
1 8 7 0
2 8 7
1 4 13 3
4 16 6 16 7
1 7 10 2
2 7 10
1 12 7 0
4 9 8 9 9
1 4 9 0
2 4 9
1 15 9 1
4 5 18 6 18
1 0 15 2
2 0 15
1 14 11 2
4 1 15 2 15
1 12 12 2
2 12 12
1 0 16 2
4 17 11 18 11
1 18 15 0
2 18 15
1 8 10 2
4 8 14 8 15
1 8 9 2
2 8 9
1 10 4 2
4 2 0 3 0
1 4 12 3
2 4 12
1 12 7 1
4 5 14 6 14
1 10 14 0
2 10 14
1 0 2 0
4 9 14 9 15
1 13 13 3
2 13 13
1 19 15 0
4 15 6 16 6
1 12 3 0
2 12 3
1 12 12 1
4 4 9 4 10
1 14 8 2
2 14 8
1 15 16 3
4 14 15 15 15
1 12 9 3
2 12 9
1 17 1 3
4 16 12 17 12
1 9 10 1
2 9 10
1 18 6 0
4 16 0 16 1
1 10 17 3
2 10 17
1 2 18 2
4 10 13 10 14
1 6 15 0
2 6 15
1 15 8 0
4 17 18 17 19
1 6 18 1
2 6 18
1 16 0 2
4 15 2 16 2
1 6 9 3
2 6 9
1 10 8 0
4 18 17 19 17
1 2 16 0
2 2 16
1 14 3 1
4 7 10 8 10
1 2 12 3
2 2 12
1 18 2 1
4 8 9 8 10
1 1 2 3
2 1 2
1 9 7 3
4 15 3 15 4
1 4 10 0
2 4 10
1 6 6 1
4 2 4 2 5
1 11 8 0
2 11 8
1 19 12 0
4 17 5 18 5
1 3 4 2
2 3 4
1 18 7 2
4 13 2 13 3
1 18 4 3
2 18 4
1 2 17 2
4 5 19 6 19
1 7 13 3
2 7 13
1 13 15 2
4 5 4 6 4
1 5 12 1
2 5 12
1 15 4 0
4 1 13 1 14
1 3 19 2
2 3 19
1 15 2 0
4 3 16 4 16
1 14 6 3
2 14 6
1 16 11 1
4 16 11 17 11
1 15 12 1
2 15 12
1 0 16 1
4 3 12 3 13
1 15 7 1
2 15 7
1 16 17 1
4 11 17 11 18
1 9 3 2
2 9 3
1 9 7 1
4 17 4 17 5
1 17 1 2
2 17 1
1 9 2 0
4 13 5 13 6
1 6 10 1
2 6 10
1 9 2 0
4 7 6 8 6
1 11 19 2
2 11 19
1 7 15 2
4 11 15 11 16
1 2 13 0
2 2 13
1 3 9 3
4 1 14 2 14
1 3 6 1
2 3 6
1 7 14 1
4 7 12 8 12
1 5 18 0
2 5 18
1 1 16 0
4 4 1 5 1
1 13 14 0
2 13 14
1 11 10 2
4 9 17 10 17
1 4 12 2
2 4 12
1 0 4 3
4 17 9 18 9
1 7 13 0
2 7 13
1 6 5 1
4 9 11 10 11
1 16 16 3
2 16 16
1 10 17 0
4 0 13 0 14
1 13 7 0
2 13 7
1 15 3 0
4 2 8 2 9
1 12 19 3
2 12 19
1 7 14 2
4 11 9 11 10
1 9 6 1
2 9 6
1 8 2 0
4 17 14 18 14
1 2 3 0
2 2 3
1 5 18 1
4 6 9 6 10
1 18 19 3
2 18 19
1 10 7 0
4 2 16 3 16
1 1 7 2
2 1 7
1 15 5 1
4 14 6 14 7
1 19 10 2
2 19 10
1 7 9 3
4 17 17 17 18
1 3 10 0
2 3 10
1 17 4 3
4 2 16 2 17
1 12 17 3
2 12 17
1 18 1 1
4 9 13 9 14
1 10 13 2
2 10 13
1 8 19 2
4 9 18 10 18
1 19 15 2
2 19 15
1 10 10 0
4 0 5 0 6
1 4 7 1
2 4 7
1 7 1 1
4 17 0 18 0
1 3 4 1
2 3 4
1 13 6 0
4 5 7 5 8
1 15 14 0
2 15 14
1 1 11 0
4 16 2 16 3
1 0 1 3
2 0 1
1 9 5 2
4 19 11 19 12
1 9 1 2
2 9 1
1 1 1 2
4 19 8 19 9
1 18 14 3
2 18 14
1 15 13 1
4 3 13 3 14
1 11 8 0
2 11 8
1 11 1 1
4 4 10 4 11
1 4 6 0
2 4 6
1 2 8 3
4 0 6 1 6
1 13 4 2
2 13 4
1 15 0 1
4 7 10 8 10
1 8 18 3
2 8 18
1 3 6 0
4 5 7 5 8
1 10 18 2
2 10 18
1 17 3 3
4 9 5 10 5
1 19 11 2
2 19 11
1 18 6 0
4 4 5 4 6
1 4 18 0
2 4 18
1 8 15 3
4 5 11 5 12
1 0 10 3
2 0 10
1 16 8 3
4 3 7 3 8
1 7 16 0
2 7 16
1 3 14 0
4 12 15 13 15
1 11 0 3
2 11 0
1 16 5 2
4 5 7 6 7
1 4 11 2
2 4 11
1 9 7 1
4 6 18 7 18
1 1 6 2
2 1 6
1 12 15 1
4 9 3 9 4
1 7 13 2
2 7 13
1 16 12 0
4 1 0 1 1
1 11 8 3
2 11 8
1 19 2 0
4 14 8 14 9
1 15 1 0
2 15 1
1 0 0 2
4 17 4 18 4
1 19 9 0
2 19 9
1 13 5 3
4 18 9 18 10
1 11 6 3
2 11 6
1 14 2 2
4 2 3 2 4
1 1 9 0
2 1 9
1 6 7 3
4 14 9 15 9
1 12 15 1
2 12 15
1 10 3 3
4 18 1 18 2
1 8 11 3
2 8 11
1 19 11 3
4 15 19 16 19
1 4 18 3
2 4 18
1 9 18 0
4 5 6 6 6
1 10 9 0
2 10 9
1 10 14 1
4 18 7 18 8
1 4 10 1
2 4 10
1 2 15 3
4 6 9 6 10
1 16 2 2
2 16 2
1 7 9 0
4 19 12 19 13
1 10 0 3
2 10 0
1 4 14 3
4 17 12 18 12
1 11 1 0
2 11 1
1 4 1 3
4 3 12 4 12
1 10 15 3
2 10 15
1 18 0 3
4 16 8 17 8
1 5 16 2
2 5 16
1 4 0 2
4 18 14 18 15
1 17 16 3
2 17 16
1 16 9 0
4 4 3 4 4
1 0 19 0
2 0 19
1 3 10 2
4 3 3 3 4
1 7 5 1
2 7 5
1 9 13 0
4 14 9 15 9
1 9 17 0
2 9 17
1 17 8 1
4 16 6 17 6
1 19 0 3
2 19 0
1 5 8 2
4 11 5 11 6
1 14 3 3
2 14 3
1 1 12 3
4 1 10 1 11
1 6 8 2
2 6 8
1 4 13 0
4 1 16 2 16
1 16 8 0
2 16 8
1 4 14 3
4 10 18 11 18
1 12 8 1
2 12 8
1 7 16 0
4 16 3 17 3
1 14 12 0
2 14 12
1 3 16 0
4 8 1 9 1
1 1 9 1
2 1 9
1 4 18 3
4 3 13 4 13
1 1 1 1
2 1 1
1 0 13 1
4 10 3 10 4
1 14 15 2
2 14 15
1 4 4 3
4 17 16 17 17
1 11 17 3
2 11 17
1 8 6 0
4 9 0 10 0
1 18 10 0
2 18 10
1 5 2 3
4 8 18 9 18
1 11 18 3
2 11 18
1 2 9 1
4 18 13 19 13
1 16 5 0
2 16 5
1 9 0 3
4 15 3 15 4
1 7 16 2
2 7 16
1 0 15 2
4 17 9 17 10
1 19 1 2
2 19 1
1 19 11 2
4 1 3 2 3
1 5 0 2
2 5 0
1 9 3 1
4 5 13 5 14
1 3 15 3
2 3 15
1 3 14 1
4 16 7 17 7
1 0 11 0
2 0 11
1 5 7 3
4 8 13 9 13
1 3 4 0
2 3 4
1 7 0 3
4 17 16 18 16
1 13 0 0
2 13 0
1 14 16 2
4 12 17 12 18
1 19 11 2
2 19 11
1 11 19 2
4 7 17 7 18
1 14 6 1
2 14 6
1 4 11 3
4 2 5 3 5
1 16 18 1
2 16 18
1 5 7 3
4 13 15 13 16
1 0 9 1
2 0 9
1 14 15 3
4 5 11 5 12
1 14 12 1
2 14 12

Story

Painter Takahashi is working on a new series of watercolor paintings. His works are highly praised for their delicate use of color, and he is especially particular about color blending. As his assistant, you are tasked with the important role of mixing and delivering the exact colors he requests, on the spot.

Because the paints used are expensive, you are expected to mix the colors with as little waste as possible. Fortunately, a list of the required colors has been provided in advance. You are asked to produce these colors in the given order, as accurately as possible and with as little waste as you can.

Problem Statement

A paint color is represented as a three-dimensional vector (C, M, Y) consisting of cyan (C), magenta (M), and yellow (Y), where 0 \leq C, M, Y \leq 1.

When you mix v_1 grams of paint with color p_1 = (C_1, M_1, Y_1) and v_2 grams of paint with color p_2 = (C_2, M_2, Y_2), you obtain (v_1 + v_2) grams of paint with color \frac{v_1 \cdot p_1 + v_2 \cdot p_2}{v_1 + v_2}.

v₁ = 4 p₁ = (1, 0, 0) + v₂ = 6 p₂ = (0, 1, 0) = v₁ + v₂ = 10 p = (0.4, 0.6, 0)

You own K types of tube paints. The i-th tube has the color (C^{\mathrm{own}}_i, M^{\mathrm{own}}_i, Y^{\mathrm{own}}_i). Using 1 gram from any tube incurs a cost of D.

Your goal is to use these tubes to produce H target colors, each exactly 1 gram, in the specified order and deliver them to the painter. The i-th target color is (C^{\mathrm{target}}_i, M^{\mathrm{target}}_i, Y^{\mathrm{target}}_i). The order of creation is fixed and cannot be changed.

The palette used for mixing paint is composed of an N \times N grid of cells. The top-left cell is at coordinate (0, 0), and the cell at i rows down and j columns to the right is (i, j).

Each cell is equipped with movable dividers between its adjacent cells in the up, down, left, and right directions. You may freely configure the initial state of these dividers.

If the divider between two adjacent cells is lowered, the two cells are said to be connected. A well is defined as a set of connected cells reachable via such connections. By moving the dividers, you can merge multiple wells or split a well into multiple separate ones.

Each well can contain at most one color of paint, and a well consisting of k cells can hold up to k grams of paint. Initially, all wells are empty.

You may perform the following operations for up to T turns:

  1. Choose any cell and any tube, and pour 1 gram of paint from the tube into the well that the cell belongs to. Let w be the remaining capacity of the well. Then, \min(w, 1) grams will actually be mixed, and the remaining 1 - \min(w, 1) grams will be immediately discarded.

  2. Choose any cell and take 1 gram of paint from the well that the cell belongs to, and deliver it to the painter. You cannot choose a cell whose well contains less than 1 gram of paint.

  3. Choose any cell and discard 1 gram of paint from the well that the cell belongs to. If less than 1 gram remains, discard all of it.

  4. Choose two adjacent cells s and t and toggle the divider between them.

    • If lowering the divider merges two wells, the paints are mixed into a single color.
    • If raising the divider splits a well into two, the paint is divided proportionally to the capacities. That is, if the well originally contained v grams of paint, and the capacities of the resulting wells are v_s and v_t for the s and t sides respectively, then the paint remaining on the s side will be v \times \frac{v_s}{v_s + v_t}, and the t side will have v \times \frac{v_t}{v_s + v_t}.

You must perform operation 2 exactly H times. If you perform it fewer or more than H times, the result will be WA.

About Floating-Point Precision

Since paint quantities are fractional values, it is difficult to strictly determine whether a well contains “at least 1 gram” for operation 2. Therefore, the judge system manages paint quantities using double-precision floating-point numbers, and the validity of operation 2 and the extracted amount are determined based on the internal value v (in grams) as follows:

  • Validity of operation

    • If v < 1 - 10^{-6}: The well is considered to contain “less than 1 gram,” and operation 2 cannot be performed.
    • If v \geq 1 - 10^{-6}: The well is considered to contain “at least 1 gram,” and operation 2 can be performed.

  • Amount extracted

    • If v \geq 1: Exactly 1 gram is extracted.
    • If 1 - 10^{-6} \leq v < 1: All of the remaining paint in the well is extracted.

The provided tools are implemented to behave exactly the same as the judge system.

Scoring

Let the color of the paint delivered to the painter in the i-th execution of operation 2 be (C_i^\mathrm{made}, M_i^\mathrm{made}, Y_i^\mathrm{made}). The total error E is defined as follows:

\[ E = \sum_{i=0}^{H-1} \sqrt{(C^{\mathrm{target}}_i - C^{\mathrm{made}}_i)^2 + (M^{\mathrm{target}}_i - M^{\mathrm{made}}_i)^2 + (Y^{\mathrm{target}}_i - Y^{\mathrm{made}}_i)^2} \]

Let V be the number of times operation 1 was performed. Then, your absolute score is calculated as:

\[ 1 + D \cdot (V - H) + \mathrm{round}(10^4 \times E) \]

The lower the absolute score, the better.

For each test case, we compute the relative score \mathrm{round}(10^9\times \frac{\mathrm{MIN}}{\mathrm{YOUR}}), where YOUR is your absolute score and MIN is the lowest absolute score among all competitors obtained on that test case. The score of the submission is the sum of the relative scores.

The final ranking will be determined by the system test with more inputs which will be run after the contest is over. In both the provisional/system test, if your submission produces illegal output or exceeds the time limit for some test cases, only the score for those test cases will be zero, and your submission will be excluded from the MIN calculation for those test cases.

The system test will be performed only for the last submission which received a result other than CE . Be careful not to make a mistake in the final submission.

Number of test cases

  • Provisional test: 50
  • System test: 2000. We will publish seeds.txt (sha256=e93b5367e87f49c8fe325dbeb0f8daa331d23481c1eb533ff032c7978e39ae04) after the contest is over.

About relative evaluation system

In both the provisional/system test, the standings will be calculated using only the last submission which received a result other than CE. Only the last submissions are used to calculate the MIN for each test case when calculating the relative scores.

The scores shown in the standings are relative, and whenever a new submission arrives, all relative scores are recalculated. On the other hand, the score for each submission shown on the submissions page is the sum of the absolute score for each test case, and the relative scores are not shown. In order to know the relative score of submission other than the latest one in the current standings, you need to resubmit it. If your submission produces illegal output or exceeds the time limit for some test cases, the score shown on the submissions page will be 0, but the standings show the sum of the relative scores for the test cases that were answered correctly.

About execution time

Execution time may vary slightly from run to run. In addition, since system tests simultaneously perform a large number of executions, it has been observed that execution time increases by several percent compared to provisional tests. For these reasons, submissions that are very close to the time limit may result in TLE in the system test. Please measure the execution time in your program to terminate the process, or have enough margin in the execution time.

Input

The input is given from Standard Input in the following format:

N K H T D
C_0^{\mathrm{own}} M_0^{\mathrm{own}} Y_0^{\mathrm{own}}
\vdots
C_{K-1}^{\mathrm{own}} M_{K-1}^{\mathrm{own}} Y_{K-1}^{\mathrm{own}}
C_0^{\mathrm{target}} M_0^{\mathrm{target}} Y_0^{\mathrm{target}}
\vdots
C_{H-1}^{\mathrm{target}} M_{H-1}^{\mathrm{target}} Y_{H-1}^{\mathrm{target}}
  • The palette size N is fixed to N = 20 for all test cases.
  • The number of tube paint types K satisfies 4 \leq K \leq 20.
  • The number of target colors H is fixed to H = 1000 for all test cases.
  • The maximum number of turns T satisfies 4000 \leq T \leq 64000.
  • The cost D for using 1 gram from a tube satisfies 10 \leq D \leq 10000.

Output

First, output the initial configuration of dividers in the following format to standard output:

v_{0,0} \cdots v_{0,N-2}
\vdots
v_{N-1,0} \cdots v_{N-1,N-2}
h_{0,0} \cdots h_{0,N-1}
\vdots
h_{N-2,0} \cdots h_{N-2,N-1}
  • v_{i,j} represents the state of the vertical divider between cell (i, j) and cell (i, j+1). If v_{i,j} = 0, the divider is lowered. If v_{i,j} = 1, the divider is raised.
  • h_{i,j} represents the state of the horizontal divider between cell (i, j) and cell (i+1, j). If h_{i,j} = 0, the divider is lowered. If h_{i,j} = 1, the divider is raised.

Next, output up to T lines of operations. The t-th line specifies the operation to be performed on turn t in one of the following formats:

  • To add 1 gram of paint from tube k (0 \leq k \leq K-1) to the well containing cell (i, j):
1 i j k
  • To extract 1 gram of paint from the well containing cell (i, j) and deliver it to the painter:
2 i j
  • To discard 1 gram of paint from the well containing cell (i, j):
3 i j
  • To toggle the divider between adjacent cells (i_1, j_1) and (i_2, j_2):
4 i_1 j_1 i_2 j_2

Show example

Input Generation

  • \mathrm{rand}(L,U): Generates a uniformly random integer between L and U, inclusive.
  • \mathrm{rand\_double}(L,U): Generates a uniformly random real number between L and U.

Generation of N, K, H, T, and D

  • N = 20
  • K = \mathrm{rand}(4,20)
  • H = 1000
  • T = \mathrm{round}(4000 \times 2^{\mathrm{rand\_double}(0,4)})
  • D = \mathrm{round}(10^{\mathrm{rand\_double}(1,4)})

Generation of tube paint (C^{\mathrm{own}}, M^{\mathrm{own}}, Y^{\mathrm{own}})

For each i, generate independently as follows:

  • C_i^{\mathrm{own}} = \mathrm{rand}(0,10^5) \times 10^{-5}
  • M_i^{\mathrm{own}} = \mathrm{rand}(0,10^5) \times 10^{-5}
  • Y_i^{\mathrm{own}} = \mathrm{rand}(0,10^5) \times 10^{-5}

Generation of target colors (C^{\mathrm{target}}, M^{\mathrm{target}}, Y^{\mathrm{target}})

The target colors are generated independently for each i as follows:

  1. Generate K values x_0, \dots, x_{K-1} using x_k = -\ln \mathrm{rand\_double}(0, 1), where \ln denotes the natural logarithm.
  2. Normalize: Let x_k' = x_k \Big/ \sum_{j=0}^{K-1} x_j.
  3. Compute the components of the target color as follows: \[ C_i^{\mathrm{target}} = \mathrm{round}\left(10^5 \times \sum_{k=0}^{K-1} x_k' C_k^\mathrm{own}\right) \times 10^{-5} \] \[ M_i^{\mathrm{target}} = \mathrm{round}\left(10^5 \times \sum_{k=0}^{K-1} x_k' M_k^\mathrm{own}\right) \times 10^{-5} \] \[ Y_i^{\mathrm{target}} = \mathrm{round}\left(10^5 \times \sum_{k=0}^{K-1} x_k' Y_k^\mathrm{own}\right) \times 10^{-5} \]

Tools (Input generator and visualizer)

Please be aware that sharing visualization results or discussing solutions/ideas during the contest is prohibited.

Sample Input 1

20 4 1000 60887 3822
0.18582 0.09589 0.89627
0.52420 0.23682 0.12026
0.25071 0.05604 0.49650
0.65334 0.67404 0.51617
0.44983 0.33494 0.51708
0.46831 0.36471 0.48477
0.50643 0.31952 0.31758
0.34193 0.20682 0.60385
0.44749 0.24562 0.32353
0.38963 0.30694 0.64772
0.41326 0.25529 0.43863
0.48102 0.28265 0.32024
0.52488 0.36664 0.34324
0.37841 0.18944 0.41168
0.29373 0.15923 0.65076
0.35448 0.20560 0.51296
0.32367 0.22647 0.69556
0.47855 0.38877 0.51374
0.31896 0.23366 0.72780
0.49895 0.43287 0.54629
0.50653 0.40515 0.43852
0.36207 0.20372 0.49564
0.43069 0.24221 0.40260
0.23646 0.14069 0.81177
0.33649 0.14485 0.47898
0.29053 0.10922 0.53120
0.41253 0.31572 0.60214
0.47525 0.36316 0.48463
0.29441 0.19318 0.71019
0.39693 0.30065 0.59040
0.47544 0.34956 0.45466
0.57420 0.53898 0.49769
0.36125 0.18511 0.46405
0.28114 0.13901 0.65753
0.42559 0.31318 0.50172
0.31850 0.14022 0.48070
0.43447 0.25413 0.37324
0.27765 0.12952 0.63338
0.42026 0.20582 0.35968
0.40867 0.35087 0.65872
0.46671 0.33422 0.45248
0.51818 0.49577 0.59932
0.38677 0.16434 0.36316
0.41071 0.25720 0.50019
0.38637 0.28906 0.59335
0.38513 0.15798 0.34108
0.33258 0.18452 0.58085
0.44418 0.33675 0.51918
0.49809 0.38033 0.42463
0.48630 0.24091 0.22993
0.33911 0.21807 0.61781
0.42081 0.25516 0.45980
0.51552 0.35164 0.33459
0.46662 0.24812 0.30811
0.31091 0.13384 0.49291
0.36123 0.18389 0.48357
0.42083 0.33545 0.57297
0.24826 0.07514 0.57140
0.48340 0.29052 0.31278
0.41422 0.28879 0.48976
0.34047 0.15474 0.49593
0.42539 0.20087 0.31734
0.61918 0.62082 0.52287
0.53754 0.46574 0.47679
0.31430 0.16010 0.57151
0.49821 0.43923 0.52764
0.37116 0.17485 0.45613
0.41968 0.33169 0.56024
0.40143 0.21709 0.42981
0.45401 0.26611 0.34206
0.25283 0.11414 0.65734
0.43559 0.23650 0.35251
0.28132 0.13919 0.61400
0.44600 0.29304 0.44414
0.29386 0.18632 0.68865
0.37793 0.17775 0.43777
0.53484 0.36935 0.32178
0.32996 0.18432 0.57826
0.45625 0.39205 0.57966
0.51740 0.32952 0.29365
0.52788 0.45634 0.49549
0.33898 0.25731 0.71951
0.44241 0.33788 0.50348
0.35541 0.21045 0.52630
0.28594 0.11714 0.55638
0.38528 0.26185 0.53964
0.36372 0.23391 0.55801
0.42212 0.18381 0.28939
0.39016 0.18518 0.43193
0.21601 0.09441 0.76809
0.27693 0.10150 0.52196
0.30610 0.19654 0.66791
0.60784 0.60530 0.52955
0.38758 0.23651 0.47152
0.47542 0.35640 0.47930
0.26975 0.08320 0.51065
0.30890 0.19992 0.68417
0.34053 0.19379 0.56401
0.36427 0.23960 0.54362
0.51527 0.24233 0.15570
0.23484 0.13811 0.81603
0.46326 0.39133 0.53309
0.42472 0.28718 0.46265
0.30960 0.11880 0.48909
0.49687 0.37474 0.41680
0.48903 0.42773 0.52723
0.44700 0.28841 0.41649
0.35855 0.28369 0.69817
0.49270 0.34811 0.38421
0.30698 0.13072 0.49701
0.27151 0.13131 0.63046
0.40535 0.27205 0.53082
0.37917 0.23776 0.56343
0.32758 0.26528 0.76626
0.28313 0.10240 0.51453
0.47578 0.41780 0.56286
0.32558 0.20836 0.64099
0.44368 0.32861 0.51686
0.31218 0.14542 0.58331
0.37343 0.23308 0.53390
0.45770 0.29193 0.37981
0.31103 0.10728 0.45058
0.40665 0.21431 0.39251
0.25911 0.09397 0.60506
0.24973 0.09796 0.64991
0.45825 0.23037 0.27616
0.45709 0.36803 0.49978
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0.58950 0.56575 0.51165
0.47425 0.42280 0.59396
0.37031 0.28643 0.66809
0.39992 0.26224 0.52901
0.46227 0.34532 0.46074
0.43827 0.35474 0.56333
0.44498 0.36417 0.57289
0.37736 0.18110 0.41376
0.55311 0.46725 0.42665
0.35034 0.20821 0.52692
0.39737 0.21857 0.44402
0.43104 0.20816 0.33172
0.48920 0.45212 0.60049
0.37451 0.31723 0.71984
0.34374 0.14189 0.43775
0.45489 0.37743 0.53356
0.45348 0.40180 0.61592
0.32133 0.16189 0.52696
0.32825 0.13263 0.44681
0.40895 0.21329 0.36803
0.37233 0.17742 0.46161
0.52394 0.42511 0.43468
0.32253 0.15357 0.51055
0.29969 0.09667 0.45085
0.25341 0.09734 0.61769
0.27932 0.15180 0.69882
0.36005 0.20781 0.50999
0.31196 0.10984 0.43977
0.28193 0.13955 0.60565
0.50417 0.35014 0.38000
0.26038 0.12824 0.67259
0.41480 0.29381 0.48724
0.43378 0.23908 0.39449
0.48483 0.41764 0.55776
0.28205 0.14281 0.65927
0.46014 0.28102 0.35235
0.40827 0.19713 0.39686
0.34640 0.14562 0.43044
0.41717 0.25807 0.43120
0.40420 0.33200 0.62206
0.31872 0.16240 0.56783
0.26598 0.10778 0.62800
0.42660 0.34036 0.60434
0.46528 0.40075 0.59202
0.40735 0.28461 0.51664
0.24592 0.06285 0.54030
0.41801 0.18572 0.31312
0.47854 0.37463 0.49618
0.25910 0.09046 0.57542
0.40059 0.32439 0.63547
0.26867 0.17774 0.76998
0.45550 0.26103 0.33966
0.41237 0.23137 0.42490
0.38005 0.17287 0.42286
0.48109 0.42505 0.58318
0.37822 0.24579 0.56843
0.36774 0.16367 0.41826
0.49560 0.46701 0.61741
0.27915 0.08692 0.49961
0.43272 0.35720 0.57006
0.34472 0.16995 0.48715
0.43280 0.29119 0.48532
0.35227 0.13964 0.38539
0.37310 0.22477 0.55345
0.30863 0.14598 0.57558
0.43410 0.37296 0.61551
0.21772 0.10418 0.78494
0.50001 0.38998 0.46669
0.29632 0.15689 0.64241
0.53039 0.34420 0.28221
0.35133 0.20119 0.53244
0.38118 0.26462 0.56244
0.37650 0.21179 0.45851
0.37190 0.26867 0.63200
0.41613 0.29434 0.48981
0.47256 0.21533 0.21715
0.31048 0.18416 0.61976
0.45811 0.23760 0.32084
0.44271 0.29448 0.45888
0.47125 0.23425 0.27073
0.32843 0.12685 0.44710
0.50711 0.44507 0.51907
0.44902 0.26738 0.39790
0.49368 0.42227 0.50748
0.32395 0.14503 0.48645
0.38505 0.31439 0.66696
0.41680 0.27656 0.45756
0.49165 0.43525 0.57232
0.32740 0.18033 0.58265
0.50179 0.44081 0.55232
0.42122 0.26143 0.44463
0.37825 0.23468 0.52403
0.25725 0.07509 0.52630
0.58452 0.51988 0.44495
0.43381 0.30339 0.50050
0.33091 0.20377 0.62190
0.33032 0.14962 0.48830
0.48351 0.43966 0.58452
0.52656 0.39266 0.39054
0.52399 0.39903 0.39315
0.30832 0.16831 0.61605
0.34926 0.27593 0.71484
0.32688 0.16799 0.56803
0.43387 0.34198 0.52984
0.40579 0.28758 0.55714
0.32288 0.18696 0.61787
0.33381 0.16196 0.49977
0.44350 0.25468 0.37761
0.57518 0.53019 0.48673
0.47684 0.37497 0.47059
0.40808 0.25671 0.45082
0.37496 0.16666 0.39693
0.27451 0.17998 0.77362
0.49003 0.39172 0.49270
0.30380 0.13521 0.56491
0.51495 0.32200 0.29475
0.22029 0.11528 0.80875
0.41768 0.36184 0.66118
0.40000 0.18926 0.36812
0.28820 0.19208 0.75692
0.29570 0.13187 0.57044
0.36683 0.27676 0.64787
0.29475 0.13965 0.55533
0.47869 0.44014 0.61303
0.39663 0.21783 0.42759
0.36641 0.27375 0.62813
0.26097 0.08057 0.53886
0.30676 0.23506 0.77758
0.38082 0.20548 0.45518
0.49711 0.37736 0.42425
0.45554 0.38151 0.53854
0.51347 0.32362 0.29327
0.30433 0.21301 0.74267
0.45121 0.23177 0.31139
0.38431 0.21927 0.49987
0.33868 0.14797 0.43176
0.46443 0.34079 0.46791
0.48905 0.41488 0.52346
0.46707 0.38509 0.55971
0.42740 0.33508 0.55888
0.34249 0.22229 0.60318
0.45079 0.34535 0.48882
0.27391 0.13729 0.65909
0.25997 0.16704 0.79268
0.54093 0.48971 0.51260
0.39670 0.23080 0.42615
0.31328 0.21474 0.69215
0.26428 0.16155 0.74977
0.47188 0.40097 0.54011
0.32815 0.15968 0.55008
0.48151 0.24252 0.24964
0.32407 0.21632 0.65625
0.53926 0.29450 0.17749
0.44975 0.19234 0.23278
0.38045 0.29245 0.62159
0.46584 0.38719 0.56459
0.39469 0.21269 0.45712
0.41016 0.22620 0.41422
0.34857 0.27457 0.69958
0.44628 0.28999 0.41277
0.40566 0.27717 0.49184
0.52020 0.42781 0.46396
0.41647 0.33541 0.58805
0.51983 0.46388 0.52052
0.39498 0.29072 0.56436
0.38372 0.30309 0.63455
0.45252 0.30901 0.45849
0.29202 0.19921 0.74297
0.60601 0.55864 0.45038
0.34788 0.16832 0.46465
0.40683 0.27655 0.48944
0.31789 0.23860 0.74934
0.49361 0.40960 0.52242
0.42762 0.18550 0.29616
0.45522 0.39590 0.58503
0.40555 0.19518 0.36071
0.32281 0.18176 0.55807
0.37546 0.23738 0.53053
0.38393 0.17563 0.39200
0.23523 0.09551 0.67909
0.38593 0.17068 0.38818
0.30520 0.17860 0.65689
0.23861 0.13959 0.80865
0.47261 0.41444 0.58368
0.43311 0.27947 0.44061
0.42875 0.33050 0.53334
0.31456 0.16524 0.59703
0.53141 0.36847 0.32234
0.31734 0.15046 0.50310
0.30975 0.15888 0.62019
0.42627 0.33811 0.58103
0.44049 0.35665 0.53961
0.54446 0.52741 0.57951
0.28283 0.14483 0.67559
0.40383 0.30278 0.59587
0.23000 0.07857 0.65997
0.45624 0.31767 0.44944
0.49734 0.44547 0.55942
0.32672 0.15928 0.57012
0.28419 0.17148 0.68652
0.42007 0.31278 0.57313
0.35042 0.18803 0.49661
0.34779 0.20573 0.59199
0.32080 0.22640 0.69593
0.34923 0.21576 0.56005
0.51396 0.43606 0.49591
0.34289 0.23377 0.63080
0.27945 0.10368 0.52394
0.53515 0.44269 0.44326
0.36720 0.19388 0.45437
0.42311 0.31915 0.50790
0.58311 0.52044 0.44438
0.53233 0.40656 0.37888
0.47415 0.36074 0.46755
0.50767 0.25877 0.19787
0.28864 0.16291 0.65309
0.44728 0.33667 0.49650
0.38031 0.27736 0.60965
0.31120 0.14395 0.58810
0.31262 0.18873 0.61311
0.32974 0.16730 0.53356
0.53484 0.49813 0.54488
0.32660 0.15681 0.48723
0.39239 0.27584 0.58787
0.34702 0.14615 0.45219
0.36605 0.17684 0.47815
0.52554 0.39146 0.37580
0.45893 0.23377 0.29367
0.46977 0.40139 0.57336
0.34210 0.21589 0.61972
0.48233 0.38401 0.49703
0.44582 0.35201 0.52477
0.21247 0.09968 0.80361
0.46089 0.38142 0.52047
0.55704 0.39775 0.30522
0.38434 0.23537 0.47198
0.42869 0.37725 0.66028
0.38515 0.19669 0.42578
0.39876 0.22046 0.40558
0.40772 0.21672 0.38397
0.29060 0.20888 0.77131
0.44554 0.35722 0.55759
0.27097 0.13904 0.67219
0.59633 0.54651 0.45178
0.33443 0.22696 0.63088
0.42552 0.32409 0.55249
0.39913 0.31685 0.64002
0.43705 0.19937 0.30907
0.42174 0.32405 0.52952
0.32003 0.18802 0.58206
0.41124 0.19173 0.32615
0.63498 0.64629 0.52028
0.41261 0.28636 0.52187
0.41527 0.19901 0.35073
0.41370 0.37219 0.69585
0.41565 0.34664 0.64131
0.38015 0.29468 0.64257
0.52786 0.45124 0.49182
0.28136 0.14916 0.67420
0.55814 0.46702 0.43073
0.44239 0.30991 0.49368
0.53772 0.50627 0.54902
0.42767 0.29168 0.48154
0.40014 0.26562 0.49595
0.50451 0.33189 0.34337
0.27284 0.11326 0.61226
0.30514 0.14201 0.55821
0.31227 0.16420 0.54576
0.34925 0.28834 0.74368
0.45321 0.28431 0.37489
0.55329 0.51408 0.51386
0.50452 0.45092 0.55650
0.31169 0.16890 0.60175
0.49053 0.22778 0.20586
0.40735 0.35201 0.67687
0.33101 0.17196 0.58589
0.19654 0.09552 0.84831
0.43485 0.32886 0.55654
0.42269 0.28630 0.46251
0.33792 0.26872 0.73404
0.40485 0.33376 0.63209
0.49386 0.33425 0.36824
0.52195 0.35180 0.32021
0.47078 0.42464 0.61150
0.48317 0.40785 0.52743
0.52917 0.46003 0.49586
0.34846 0.21692 0.58468
0.35122 0.18886 0.50916
0.47949 0.42467 0.58903
0.44856 0.34103 0.52612
0.34976 0.23528 0.63677
0.38364 0.21810 0.50030
0.45403 0.34884 0.48296

Sample Output 1

1 0 1 1 1 1 0 0 0 0 0 1 0 1 1 1 0 0 0
1 1 1 1 1 0 0 0 0 1 0 1 0 0 0 1 1 0 1
0 0 0 1 0 0 1 0 0 1 1 0 1 0 1 0 1 0 0
0 1 0 1 1 0 0 1 1 0 1 0 1 1 0 1 1 0 0
1 1 1 1 1 1 0 0 0 0 1 1 1 0 0 0 0 1 1
1 1 0 0 1 0 0 1 1 1 0 0 0 1 0 0 1 0 0
0 1 0 1 0 1 0 1 0 1 1 1 0 1 1 0 1 0 1
1 1 0 0 1 1 1 0 1 1 0 1 1 1 1 1 1 0 1
0 0 0 0 1 1 0 1 1 0 1 1 0 0 1 1 0 1 1
0 0 0 0 0 0 0 1 1 1 0 1 1 0 0 1 0 0 0
0 1 0 0 1 0 0 1 0 1 0 1 1 0 0 1 1 0 1
0 1 1 0 1 0 1 0 1 0 0 1 1 0 1 0 0 1 1
1 1 1 1 1 0 1 0 1 1 0 0 1 0 1 1 1 0 0
0 1 0 1 0 1 1 0 0 1 1 1 1 1 0 1 0 0 1
1 1 0 1 0 0 0 0 1 1 1 1 1 1 0 0 1 1 1
0 0 1 0 1 1 1 1 0 1 1 1 0 1 0 0 0 1 1
0 0 1 1 0 1 0 0 0 1 1 0 0 0 0 1 0 0 0
1 0 0 0 1 1 0 1 0 1 1 0 1 0 1 1 0 0 1
0 0 0 0 0 0 1 1 0 0 0 1 1 1 1 1 0 1 1
0 0 0 0 1 0 1 1 1 1 0 1 0 1 1 0 0 1 0
1 0 1 0 0 1 1 1 0 0 1 1 0 1 0 1 0 0 1 1
1 1 0 1 0 0 0 1 0 1 0 1 1 1 1 1 0 1 0 0
1 1 1 0 1 0 0 0 0 0 1 0 0 0 0 1 0 1 0 0
0 0 1 1 1 0 1 0 0 1 1 1 1 0 1 1 1 1 0 1
0 0 0 0 1 1 1 0 1 1 0 0 0 1 1 0 1 1 1 1
1 0 1 1 1 0 0 0 0 0 0 1 1 0 1 0 1 1 1 0
0 1 0 0 1 0 1 1 1 0 0 0 0 1 0 0 0 1 0 1
0 0 0 0 0 0 0 1 1 1 1 1 0 1 0 0 1 1 1 0
1 1 1 0 0 1 1 1 1 1 0 1 1 1 1 0 0 1 1 1
0 1 0 1 1 1 0 1 0 0 1 0 1 0 1 1 1 1 0 0
0 1 0 0 1 0 0 0 1 1 1 0 0 0 0 1 1 0 1 0
0 0 1 0 0 0 1 1 0 0 1 1 0 0 1 0 0 1 1 0
0 1 0 0 0 1 1 0 1 1 0 0 0 0 0 1 1 1 1 1
1 1 0 1 0 0 1 0 1 1 1 1 1 1 1 0 0 1 0 0
0 0 0 0 1 1 0 0 1 0 1 1 1 0 0 0 1 0 0 0
0 1 1 1 1 0 0 1 1 0 0 1 0 1 0 0 1 1 1 1
1 1 0 1 0 1 0 1 1 0 0 1 1 0 1 1 1 1 0 0
1 1 0 1 0 0 0 0 1 1 0 1 0 0 1 0 0 0 0 0
0 1 1 1 1 0 0 0 1 1 0 1 1 1 1 0 0 1 1 0
1 5 18 2
4 13 3 14 3
1 19 2 1
2 19 2
1 1 19 3
4 12 1 13 1
1 10 10 2
2 10 10
1 17 9 2
4 15 10 16 10
1 14 2 0
2 14 2
1 8 7 3
4 15 16 15 17
1 3 9 0
2 3 9
1 10 0 3
4 2 8 3 8
1 18 12 1
2 18 12
1 4 4 3
4 2 4 2 5
1 18 5 0
2 18 5
1 5 10 3
4 5 3 5 4
1 13 1 1
2 13 1
1 1 11 0
4 16 8 17 8
1 5 16 3
2 5 16
1 10 0 1
4 12 10 13 10
1 8 3 1
2 8 3
1 0 9 3
4 14 9 15 9
1 7 5 1
2 7 5
1 11 10 3
4 14 11 15 11
1 14 13 3
2 14 13
1 12 10 0
4 9 12 9 13
1 12 18 1
2 12 18
1 2 17 0
4 19 18 19 19
1 9 9 0
2 9 9
1 7 13 2
4 11 6 11 7
1 12 2 0
2 12 2
1 0 12 2
4 14 4 15 4
1 19 8 3
2 19 8
1 9 15 2
4 4 15 5 15
1 14 3 0
2 14 3
1 0 19 2
4 19 4 19 5
1 8 8 2
2 8 8
1 0 12 0
4 14 6 14 7
1 0 7 1
2 0 7
1 17 12 1
4 14 16 15 16
1 6 11 1
2 6 11
1 3 5 0
4 16 19 17 19
1 0 12 0
2 0 12
1 9 8 1
4 10 13 11 13
1 10 2 2
2 10 2
1 15 2 0
4 0 0 1 0
1 11 16 3
2 11 16
1 2 11 3
4 5 5 6 5
1 7 1 0
2 7 1
1 15 4 3
4 17 7 17 8
1 15 8 3
2 15 8
1 7 18 1
4 4 3 4 4
1 5 10 3
2 5 10
1 17 15 3
4 3 17 3 18
1 10 9 0
2 10 9
1 4 5 2
4 0 11 1 11
1 11 9 3
2 11 9
1 5 16 2
4 7 17 8 17
1 8 3 1
2 8 3
1 14 13 2
4 8 12 9 12
1 8 1 0
2 8 1
1 10 10 3
4 2 7 2 8
1 7 5 3
2 7 5
1 0 4 2
4 12 1 13 1
1 6 11 1
2 6 11
1 6 12 2
4 13 5 14 5
1 8 0 2
2 8 0
1 17 13 1
4 4 0 4 1
1 17 5 1
2 17 5
1 10 0 3
4 13 14 13 15
1 8 9 3
2 8 9
1 1 18 3
4 5 10 6 10
1 4 18 1
2 4 18
1 13 2 2
4 5 16 5 17
1 2 6 2
2 2 6
1 18 9 1
4 4 4 5 4
1 4 19 3
2 4 19
1 8 13 1
4 3 6 4 6
1 5 10 2
2 5 10
1 4 2 2
4 4 11 5 11
1 18 15 0
2 18 15
1 15 9 0
4 8 18 9 18
1 13 19 2
2 13 19
1 18 8 3
4 15 4 15 5
1 5 6 3
2 5 6
1 15 2 1
4 10 4 10 5
1 18 13 1
2 18 13
1 14 15 1
4 0 16 1 16
1 8 9 0
2 8 9
1 15 0 2
4 9 16 9 17
1 9 18 1
2 9 18
1 8 5 1
4 1 3 2 3
1 16 1 0
2 16 1
1 18 18 2
4 17 2 17 3
1 1 2 1
2 1 2
1 16 10 2
4 6 6 7 6
1 12 13 0
2 12 13
1 9 17 1
4 11 3 11 4
1 8 7 2
2 8 7
1 15 3 0
4 8 10 8 11
1 0 5 2
2 0 5
1 5 19 3
4 0 18 1 18
1 8 6 3
2 8 6
1 11 16 0
4 10 13 11 13
1 14 15 3
2 14 15
1 16 16 2
4 16 17 16 18
1 6 7 0
2 6 7
1 8 10 1
4 4 18 5 18
1 8 15 0
2 8 15
1 15 12 1
4 3 17 3 18
1 4 4 1
2 4 4
1 18 11 1
4 3 4 3 5
1 1 14 3
2 1 14
1 12 8 2
4 18 3 18 4
1 7 1 2
2 7 1
1 17 10 2
4 5 14 5 15
1 5 16 1
2 5 16
1 4 12 2
4 12 0 13 0
1 18 18 2
2 18 18
1 1 8 2
4 4 1 4 2
1 5 14 2
2 5 14
1 9 9 3
4 18 13 18 14
1 5 15 1
2 5 15
1 11 4 2
4 3 1 3 2
1 8 17 2
2 8 17
1 3 2 2
4 10 15 11 15
1 3 18 2
2 3 18
1 10 4 0
4 10 12 11 12
1 11 14 3
2 11 14
1 11 12 3
4 9 6 10 6
1 17 10 2
2 17 10
1 3 12 3
4 13 16 13 17
1 9 6 3
2 9 6
1 0 5 1
4 6 8 6 9
1 6 2 0
2 6 2
1 1 6 1
4 13 4 13 5
1 13 11 0
2 13 11
1 7 1 0
4 10 18 11 18
1 4 2 3
2 4 2
1 8 11 1
4 12 15 12 16
1 6 17 1
2 6 17
1 8 15 2
4 9 6 9 7
1 19 2 1
2 19 2
1 19 2 0
4 2 11 2 12
1 4 4 1
2 4 4
1 16 0 0
4 9 12 10 12
1 4 17 3
2 4 17
1 18 3 3
4 13 1 13 2
1 13 13 0
2 13 13
1 12 7 2
4 7 11 8 11
1 11 4 0
2 11 4
1 17 12 0
4 1 10 2 10
1 11 3 0
2 11 3
1 12 0 1
4 7 5 7 6
1 4 5 0
2 4 5
1 17 7 3
4 8 9 8 10
1 0 6 2
2 0 6
1 7 12 3
4 0 0 0 1
1 11 17 3
2 11 17
1 17 16 1
4 5 12 6 12
1 5 0 1
2 5 0
1 11 0 2
4 5 15 5 16
1 11 4 3
2 11 4
1 6 14 3
4 18 8 19 8
1 3 7 0
2 3 7
1 15 5 2
4 13 19 14 19
1 12 19 0
2 12 19
1 3 16 1
4 13 11 13 12
1 16 4 2
2 16 4
1 15 4 3
4 14 17 14 18
1 4 14 1
2 4 14
1 2 2 1
4 2 7 3 7
1 7 9 0
2 7 9
1 19 3 1
4 4 15 4 16
1 10 14 2
2 10 14
1 10 19 2
4 10 15 11 15
1 8 12 0
2 8 12
1 12 0 3
4 13 16 14 16
1 7 16 1
2 7 16
1 8 4 1
4 15 3 16 3
1 13 18 3
2 13 18
1 19 19 2
4 6 8 7 8
1 12 17 3
2 12 17
1 15 13 3
4 11 9 12 9
1 18 17 2
2 18 17
1 19 12 0
4 13 12 14 12
1 2 1 2
2 2 1
1 9 18 0
4 0 1 1 1
1 9 8 1
2 9 8
1 0 10 2
4 8 16 8 17
1 12 13 2
2 12 13
1 6 14 0
4 15 11 15 12
1 13 4 1
2 13 4
1 4 15 0
4 14 14 14 15
1 16 18 0
2 16 18
1 5 2 3
4 2 19 3 19
1 11 0 0
2 11 0
1 3 7 0
4 15 4 15 5
1 12 15 0
2 12 15
1 9 12 2
4 0 3 1 3
1 17 16 1
2 17 16
1 12 19 3
4 8 0 9 0
1 18 16 2
2 18 16
1 14 1 0
4 15 13 15 14
1 11 4 0
2 11 4
1 11 5 0
4 18 2 18 3
1 13 12 0
2 13 12
1 3 6 2
4 3 15 3 16
1 1 6 1
2 1 6
1 3 18 3
4 9 0 10 0
1 14 13 2
2 14 13
1 3 1 2
4 10 12 11 12
1 12 12 1
2 12 12
1 9 17 1
4 18 7 18 8
1 16 18 0
2 16 18
1 12 8 2
4 14 17 14 18
1 7 15 2
2 7 15
1 8 18 3
4 6 3 6 4
1 5 13 0
2 5 13
1 16 1 2
4 4 9 4 10
1 16 8 2
2 16 8
1 5 12 1
4 15 3 16 3
1 8 9 2
2 8 9
1 8 4 1
4 18 6 19 6
1 12 2 0
2 12 2
1 6 2 1
4 6 8 7 8
1 3 9 0
2 3 9
1 18 19 3
4 6 1 7 1
1 13 7 2
2 13 7
1 0 14 3
4 12 13 13 13
1 5 18 3
2 5 18
1 14 9 3
4 18 9 19 9
1 6 6 3
2 6 6
1 5 4 3
4 0 6 0 7
1 14 16 2
2 14 16
1 0 5 1
4 9 15 10 15
1 0 7 0
2 0 7
1 3 4 2
4 14 17 15 17
1 9 17 3
2 9 17
1 0 4 3
4 10 17 10 18
1 10 12 3
2 10 12
1 1 12 0
4 1 17 2 17
1 14 17 0
2 14 17
1 8 14 1
4 15 8 16 8
1 17 19 0
2 17 19
1 1 2 1
4 4 6 4 7
1 5 2 2
2 5 2
1 12 7 2
4 15 11 15 12
1 3 16 3
2 3 16
1 16 15 1
4 15 15 16 15
1 17 16 2
2 17 16
1 8 14 0
4 5 3 6 3
1 8 13 0
2 8 13
1 11 1 0
4 15 15 15 16
1 14 6 3
2 14 6
1 2 9 1
4 9 11 9 12
1 13 13 0
2 13 13
1 16 19 0
4 18 18 18 19
1 7 16 1
2 7 16
1 7 9 1
4 11 9 12 9
1 3 8 2
2 3 8
1 2 16 3
4 14 16 15 16
1 13 13 3
2 13 13
1 11 14 2
4 12 10 12 11
1 4 2 0
2 4 2
1 1 4 2
4 6 1 6 2
1 15 0 3
2 15 0
1 1 15 0
4 16 11 17 11
1 5 5 2
2 5 5
1 5 2 3
4 4 11 4 12
1 2 9 1
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1 10 12 2
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4 17 19 18 19
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1 9 5 3
4 2 9 2 10
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1 13 13 1
4 14 5 14 6
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4 14 13 14 14
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4 18 7 18 8
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4 9 16 10 16
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1 10 2 1
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4 3 14 4 14
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4 1 12 2 12
1 17 10 2
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1 6 6 3
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4 15 17 16 17
1 12 16 0
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4 12 12 12 13
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4 9 8 9 9
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1 12 13 3
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4 13 11 14 11
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4 14 13 14 14
1 11 6 3
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4 14 16 14 17
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4 5 7 5 8
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1 12 7 3
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1 1 2 0
2 1 2
1 19 10 2
4 9 16 10 16
1 17 17 3
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1 12 11 0
4 7 9 8 9
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