Problem Statement

N players, who are numbered 1, \ldots, N, have played a game. Player i has scored A_i, and a player with a smaller score ranks higher.

The player who ranks the second lowest will receive a booby prize. Who is this player? Answer with an integer representing the player.

Constraints

• 2 \leq N \leq 2\times 10^5
• 1 \leq A_i \leq 10^9
• A_i are distinct.
• All values in input are integers.

Sample Input 1

6
1 123 12345 12 1234 123456

Sample Output 1

3

It is Player 3 who ranks fifth among the six players.

Sample Input 2

5
3 1 4 15 9

Sample Output 2

5

Problem Statement

Let us call a string consisting of uppercase and lowercase English alphabets a wonderful string if all of the following conditions are satisfied:

• The string contains an uppercase English alphabet.
• The string contains a lowercase English alphabet.
• All characters in the string are pairwise distinct.

For example, AtCoder and Aa are wonderful strings, while atcoder and Perfect are not.

Given a string S, determine if S is a wonderful string.

Constraints

• 1 \le |S| \le 100
• S is a string consisting of uppercase and lowercase English alphabets.

Sample Input 1

AtCoder

Sample Output 1

Yes

AtCoder is a wonderful string because it contains an uppercase English alphabet, a lowercase English alphabet, and all characters in the string are pairwise distinct.

Sample Input 2

Aa

Sample Output 2

Yes

Note that A and a are different characters. This string is a wonderful string.

Sample Input 3

atcoder

Sample Output 3

No

It is not a wonderful string because it does not contain an uppercase English alphabet.

Sample Input 4

Perfect

Sample Output 4

No

It is not a wonderful string because the 2-nd and the 5-th characters are the same.

Problem Statement

In AtCoder Land, there are N popcorn stands numbered 1 to N. They have M different flavors of popcorn, labeled 1, 2, \dots, M, but not every stand sells all flavors of popcorn.

Takahashi has obtained information about which flavors of popcorn are sold at each stand. This information is represented by N strings S_1, S_2, \dots, S_N of length M. If the j-th character of S_i is o, it means that stand i sells flavor j of popcorn. If it is x, it means that stand i does not sell flavor j. Each stand sells at least one flavor of popcorn, and each flavor of popcorn is sold at least at one stand.

Takahashi wants to try all the flavors of popcorn but does not want to move around too much. Determine the minimum number of stands Takahashi needs to visit to buy all the flavors of popcorn.

Constraints

• N and M are integers.
• 1 \leq N, M \leq 10
• Each S_i is a string of length M consisting of o and x.
• For every i (1 \leq i \leq N), there is at least one o in S_i.
• For every j (1 \leq j \leq M), there is at least one i such that the j-th character of S_i is o.

Sample Input 1

3 5
oooxx
xooox
xxooo

Sample Output 1

2

By visiting the 1st and 3rd stands, you can buy all the flavors of popcorn. It is impossible to buy all the flavors from a single stand, so the answer is 2.

Sample Input 2

3 2
oo
ox
xo

Sample Output 2

1

Sample Input 3

8 6
xxoxxo
xxoxxx
xoxxxx
xxxoxx
xxoooo
xxxxox
xoxxox
oxoxxo

Sample Output 3

3

Problem Statement

Takahashi is standing at the coordinate 0 on a number line.

He will now perform N jumps. In the i-th jump (1 \leq i \leq N), he moves a_i or b_i in the positive direction.

Is it possible for him to be at the coordinate X after N jumps?

Constraints

• 1 \leq N \leq 100
• 1 \leq a_i \lt b_i \leq 100 \, (1 \leq i \leq N)
• 1 \leq X \leq 10000
• All values in input are integers.

Sample Input 1

2 10
3 6
4 5

Sample Output 1

Yes

By moving b_1 (= 6) in the first jump and a_2 (= 4) in the second jump, he can be at the coordinate X (= 10).

Sample Input 2

2 10
10 100
10 100

Sample Output 2

No

He can be at the coordinate X (= 10) after the first jump, but not after all jumps.

Sample Input 3

4 12
1 8
5 7
3 4
2 6

Sample Output 3

Yes

Problem Statement

You are given a positive integer N, and an integer A_{x,y,z} for each triple of integers (x, y, z) such that 1 \leq x, y, z \leq N.

You will be given Q queries in the following format, which must be processed in order.

For the i-th query (1 \leq i \leq Q), you are given a tuple of integers (Lx_i, Rx_i, Ly_i, Ry_i, Lz_i, Rz_i) such that 1 \leq Lx_i \leq Rx_i \leq N, 1 \leq Ly_i \leq Ry_i \leq N, and 1 \leq Lz_i \leq Rz_i \leq N. Find:

\displaystyle{\sum_{x=Lx_i}^{Rx_i} \sum_{y=Ly_i}^{Ry_i} \sum_{z=Lz_i}^{Rz_i} A_{x,y,z}}.

Constraints

• 1 \leq N \leq 100
• 1 \leq Q \leq 2 \times 10^{5}
• 0 \leq A_{x,y,z} \leq 999 (1 \leq x, y, z \leq N)
• 1 \leq Lx_i \leq Rx_i \leq N (1 \leq i \leq Q)
• 1 \leq Ly_i \leq Ry_i \leq N (1 \leq i \leq Q)
• 1 \leq Lz_i \leq Rz_i \leq N (1 \leq i \leq Q)
• All input values are integers.

Sample Input 1

2
1 2
3 4
5 6
7 8
2
1 2 2 2 1 1
2 2 1 2 1 2

Sample Output 1

10
26

For the 1st query, the sought value is A_{1,2,1} + A_{2,2,1} = 3 + 7 = 10. Thus, print 10.

For the 2nd query, the sought value is A_{2,1,1} + A_{2,1,2} + A_{2,2,1} + A_{2,2,2} = 5 + 6 + 7 + 8 = 26. Thus, print 26.

Sample Input 2

3
733 857 714
956 208 257
123 719 648
840 881 245
245 112 746
306 942 694
58 870 849
13 208 789
687 906 783
8
3 3 3 3 1 1
1 3 2 3 3 3
2 2 2 3 1 1
1 3 1 1 1 1
2 3 2 3 2 3
1 2 1 1 1 2
3 3 2 2 1 3
1 2 2 3 2 3

Sample Output 2

687
3917
551
1631
5180
3311
1010
4326