Problem Statement

Takahashi, a young baseball enthusiast, has been a very good boy this year, so Santa has decided to give him a bat or a glove, whichever is more expensive.

If a bat costs B yen and a glove costs G yen (B\neq G), which one will Santa give to Takahashi?

Constraints

• B and G are different integers between 1 and 1000, inclusive.

Sample Input 1

300 100

Sample Output 1

Bat

The bat is more expensive than the glove, so Santa will give Takahashi the bat.

Sample Input 2

334 343

Sample Output 2

Glove

The glove is more expensive than the bat, so Santa will give Takahashi the glove.

Problem Statement

There is a grid with H horizontal rows and W vertical columns. Let (i,j) denote the square at the i-th row from the top and the j-th column from the left.
Find the number of squares that share a side with Square (R, C).

Here, two squares (a,b) and (c,d) are said to share a side if and only if |a-c|+|b-d|=1 (where |x| denotes the absolute value of x).

Constraints

• All values in input are integers.
• 1 \le R \le H \le 10
• 1 \le C \le W \le 10

Sample Input 1

3 4
2 2

Sample Output 1

4

We will describe Sample Inputs/Outputs 1,2, and 3 at once below Sample Output 3.

Sample Input 2

3 4
1 3

Sample Output 2

3

Sample Input 3

3 4
3 4

Sample Output 3

2

When H=3 and W=4, the grid looks as follows.

• For Sample Input 1, there are 4 squares adjacent to Square (2,2).
• For Sample Input 2, there are 3 squares adjacent to Square (1,3).
• For Sample Input 3, there are 2 squares adjacent to Square (3,4).

Sample Input 4

1 10
1 5

Sample Output 4

2

Sample Input 5

8 1
8 1

Sample Output 5

1

Sample Input 6

1 1
1 1

Sample Output 6

0

Problem Statement

There are N people, called Person 1, Person 2, \ldots, Person N.

The parent of Person i (2 \le i \le N) is Person P_i. Here, it is guaranteed that P_i < i.

How many generations away from Person N is Person 1?

Constraints

• 2 \le N \le 50
• 1 \le P_i < i(2 \le i \le N)
• All values in input are integers.

Sample Input 1

3
1 2

Sample Output 1

2

Person 2 is a parent of Person 3, and thus is one generation away from Person 3.

Person 1 is a parent of Person 2, and thus is two generations away from Person 3.

Therefore, the answer is 2.

Sample Input 2

10
1 2 3 4 5 6 7 8 9

Sample Output 2

9

Problem Statement

We have 4 cards with an integer 1 written on it, 4 cards with 2, \ldots, 4 cards with N, for a total of 4N cards.

Takahashi shuffled these cards, removed one of them, and gave you a pile of the remaining 4N-1 cards. The i-th card (1 \leq i \leq 4N - 1) of the pile has an integer A_i written on it.

Find the integer written on the card removed by Takahashi.

Constraints

• 1 \leq N \leq 10^5
• 1 \leq A_i \leq N \, (1 \leq i \leq 4N - 1)
• For each k \, (1 \leq k \leq N), there are at most 4 indices i such that A_i = k.
• All values in input are integers.

Sample Input 1

3
1 3 2 3 3 2 2 1 1 1 2

Sample Output 1

3

Takahashi removed a card with 3 written on it.

Sample Input 2

1
1 1 1

Sample Output 2

1

Sample Input 3

4
3 2 1 1 2 4 4 4 4 3 1 3 2 1 3

Sample Output 3

2

Problem Statement

There is a slot machine with N reels.
The placement of symbols on the i-th reel is represented by a string S_i of length 10 containing each of 0, 1, \ldots, 9 exactly once.

Each reel has a corresponding button. For each non-negative integer t, Takahashi can press one of the buttons of his choice (or do nothing) t seconds after the reels start spinning.
If the button for the i-th reel is pressed t seconds after the start of the spin, the i-th reel will stop to display the ((t\bmod{10})+1)-th character of S_i.
Here, t\bmod{10} denotes the remainder when t is divided by 10.

Takahashi wants to stop all reels to make them display the same character.
Find the minimum number of seconds needed to achieve his objective after the start of the spin.

Constraints

• 2\leq N\leq 100
• N is an integer.
• S_i is a string of length 10 containing each of 0, 1, \ldots, 9 exactly once.

Sample Input 1

3
1937458062
8124690357
2385760149

Sample Output 1

6

Takahashi can make all reels display 8 in 6 seconds after the start of the spin by stopping them as follows.

• 0 seconds after the start of the spin, press the button for the 2-nd reel, making it stop to display the ((0\bmod{10})+1=1)-st character of S_2, 8.
• 2 seconds after the start of the spin, press the button for the 3-rd reel, making it stop to display the ((2\bmod{10})+1=3)-rd character of S_3, 8.
• 6 seconds after the start of the spin, press the button for the 1-st reel, making it stop to display the ((6\bmod{10})+1=7)-th character of S_1, 8.

There is no way to make all reels display the same character in five seconds or less, so the answer is 6.

Sample Input 2

5
0123456789
0123456789
0123456789
0123456789
0123456789

Sample Output 2

40

Note that he must stop all reels to make them display the same character.

Problem Statement

We have a grid with H horizontal rows and W vertical columns. (i, j) denotes the square at the i-th row from the top and j-th column from the left.
(i,j) has a character G_{i,j} written on it. G_{i,j} is U, D, L, or R.

You are initially at (1,1). You repeat the following operation until you cannot make a move.

Let (i,j) be the square you are currently at.
If G_{i,j} is U and i \neq 1, move to (i-1,j).
If G_{i,j} is D and i \neq H, move to (i+1,j).
If G_{i,j} is L and j \neq 1, move to (i,j-1).
If G_{i,j} is R and j \neq W, move to (i,j+1).
Otherwise, you cannot make a move.

Print the square you end up at when you cannot make a move.
If you indefinitely repeat moving, print -1 instead.

Constraints

• 1 \leq H, W \leq 500
• G_{i,j} is U, D, L, or R.
• H and W are integers.

Sample Input 1

2 3
RDU
LRU

Sample Output 1

1 3

You will move as (1, 1) \to (1, 2) \to (2, 2) \to (2, 3) \to (1, 3), ending up here, so the answer is (1, 3).

Sample Input 2

2 3
RRD
ULL

Sample Output 2

-1

You will indefinitely repeat moving as (1, 1) \to (1, 2) \to (1, 3) \to (2, 3) \to (2, 2) \to (2, 1) \to (1, 1) \to (1, 2) \to \dots, so -1 should be printed in this case.

Sample Input 3

9 44
RRDDDDRRRDDDRRRRRRDDDRDDDDRDDRDDDDDDRRDRRRRR
RRRDLRDRDLLLLRDRRLLLDDRDLLLRDDDLLLDRRLLLLLDD
DRDLRLDRDLRDRLDRLRDDLDDLRDRLDRLDDRLRRLRRRDRR
DDLRRDLDDLDDRLDDLDRDDRDDDDRLRRLRDDRRRLDRDRDD
RDLRRDLRDLLLLRRDLRDRRDRRRDLRDDLLLLDDDLLLLRDR
RDLLLLLRDLRDRLDDLDDRDRRDRLDRRRLDDDLDDDRDDLDR
RDLRRDLDDLRDRLRDLDDDLDDRLDRDRDLDRDLDDLRRDLRR
RDLDRRLDRLLLLDRDRLLLRDDLLLLLRDRLLLRRRRLLLDDR
RRRRDRDDRRRDDRDDDRRRDRDRDRDRRRRRRDDDRDDDDRRR

Sample Output 3

9 5

Problem Statement

Takahashi will toss a coin N times. He also has a counter, which initially shows 0.

Depending on the result of the i-th coin toss, the following happens:

• If it heads: Takahashi increases the counter's value by 1 and receives X_i yen (Japanese currency).
• If it tails: he resets the counter's value to 0, without receiving money.

Additionally, there are M kinds of streak bonuses. The i-th kind of streak bonus awards Y_i yen each time the counter shows C_i.

Find the maximum amount of money that Takahashi can receive.

Constraints

• 1\leq M\leq N\leq 5000
• 1\leq X_i\leq 10^9
• 1\leq C_i\leq N
• 1\leq Y_i\leq 10^9
• C_1,C_2,\ldots,C_M are all different.
• All values in input are integers.

Sample Input 1

6 3
2 7 1 8 2 8
2 10
3 1
5 5

Sample Output 1

48

If he gets head, head, tail, head, head, head, in this order, the following amounts of money are awarded.

• In the 1-st coin toss, the coin heads. Change the counter's value from 0 to 1 and receive 2 yen.
• In the 2-nd coin toss, the coin heads. Change the counter's value from 1 to 2 and receive 7 yen. Additionally, get 10 yen as a streak bonus.
• In the 3-rd coin toss, the coin tails. Change the counter's value from 2 to 0.
• In the 4-th coin toss, the coin heads. Change the counter's value from 0 to 1 and receive 8 yen.
• In the 5-th coin toss, the coin heads. Change the counter's value from 1 to 2 and receive 2 yen. Additionally, get 10 yen as a streak bonus.
• In the 6-th coin toss, the coin heads. Change the counter's value from 2 to 3 and receive 8 yen. Additionally, get 1 yen as a streak bonus.

In this case, Takahashi receives 2+(7+10)+0+8+(2+10)+(8+1)=48 yen in total, which is the maximum possible.
Note that streak bonuses are awarded any number of times each time the counter shows C_i.
As a side note, if he gets head in all 6 coin tosses, he only receives 2+(7+10)+(1+1)+8+(2+5)+8=44 yen, which is not the maximum.

Sample Input 2

3 2
1000000000 1000000000 1000000000
1 1000000000
3 1000000000

Sample Output 2

5000000000

Note that the answer may not fit into a 32-bit integer type.

Problem Statement

We have a connected undirected graph with N vertices and M edges.
The vertices are numbered 1 through N, and the edges are numbered 1 through M. Edge i connects Vertices A_i and B_i.

Takahashi is going to remove zero or more edges from this graph.

When removing Edge i, a reward of C_i is given if C_i \geq 0, and a fine of |C_i| is incurred if C_i<0.

Find the maximum total reward that Takahashi can get when the graph must be connected after removing edges.

Constraints

• 2 \leq N \leq 2\times 10^5
• N-1 \leq M \leq 2\times 10^5
• 1 \leq A_i,B_i \leq N
• -10^9 \leq C_i \leq 10^9
• The given graph is connected.
• All values in input are integers.

Sample Input 1

4 5
1 2 1
1 3 1
1 4 1
3 2 2
4 2 2

Sample Output 1

4

Removing Edges 4 and 5 yields a total reward of 4. You cannot get any more, so the answer is 4.

Sample Input 2

3 3
1 2 1
2 3 0
3 1 -1

Sample Output 2

1

There may be edges that give a negative reward when removed.

Sample Input 3

2 3
1 2 -1
1 2 2
1 1 3

Sample Output 3

5

There may be multi-edges and self-loops.

Problem Statement

Given are two sequences of N integers each: A = (A_1, A_2, \ldots, A_N) and B = (B_1, B_2 \ldots, B_N).

On the sequence A, you can do the two operations below any number of times (possibly zero) in any order.

• Choose an integer i satisfying 1 \leq i \leq N, and increase or decrease A_i by 1, for the cost of X yen (Japanese currency).
• Choose an integer i satisfying 1 \leq i \leq N-1, and swap the values of A_i and A_{i+1}, for the cost of Y yen.

Print the minimum total cost needed to make the sequence A equal the sequence B by repeating the above.

Constraints

• 2 \leq N \leq 18
• 1 \leq X \leq 10^8
• 1 \leq Y \leq 10^{16}
• 1 \leq A_i, B_i \leq 10^8
• All values in input are integers.

Sample Input 1

4 3 5
4 2 5 2
6 4 2 1

Sample Output 1

16

Initialy, we have A = (4, 2, 5, 2).
The following sequence of operations makes A equal B.

• Pay X = 3 yen to increase the value of A_3 by 1, making A = (4, 2, 6, 2).
• Pay Y = 5 yen to swap the values of A_2 and A_3, making A = (4, 6, 2, 2).
• Pay Y = 5 yen to swap the values of A_1 and A_2, making A = (6, 4, 2, 2).
• Pay X = 3 yen to decrease the value of A_4 by 1, making A = (6, 4, 2, 1).

The total cost of these operations is 3+5+5+3 = 16 yen, which is the minimum possible.

Sample Input 2

5 12345 6789
1 2 3 4 5
1 2 3 4 5

Sample Output 2

0

A and B are equal from the beginning, so no operation is needed.

Sample Input 3

18 20719114 5117250357733867
10511029 36397527 63027379 44706927 47672230 79861204 57882493 42931589 51053644 52300688 43971370 26515475 62139996 41282303 34022578 12523039 6696497 64922712
14720753 4621362 25269832 91410838 86751784 32741849 6602693 60719353 28911226 88280613 18745325 80675202 34289776 37849132 99280042 73760634 43897718 40659077

Sample Output 3

13104119429316474

Note that values in input or output may not fit into 32-bit integer types.