Problem Statement

Takahashi is exploring a cave in a video game.

The cave consists of N rooms arranged in a row. The rooms are numbered Room 1,2,\ldots,N from the entrance.

Takahashi is initially in Room 1, and the time limit is T.
For each 1 \leq i \leq N-1, he may consume a time of A_i to move from Room i to Room (i+1). There is no other way to move between rooms. He cannot make a move that makes the time limit 0 or less.

There are M bonus rooms in the cave. The i-th bonus room is Room X_i; when he arrives at the room, the time limit increases by Y_i.

Can Takahashi reach Room N?

Constraints

• 2 \leq N \leq 10^5
• 0 \leq M \leq N-2
• 1 \leq T \leq 10^9
• 1 \leq A_i \leq 10^9
• 1 < X_1 < \ldots < X_M < N
• 1 \leq Y_i \leq 10^9
• All values in input are integers.

Sample Input 1

4 1 10
5 7 5
2 10

Sample Output 1

Yes

• Takahashi is initially in Room 1, and the time limit is 10.
• He consumes a time of 5 to move to Room 2. Now the time limit is 5. Then, the time limit increases by 10; it is now 15.
• He consumes a time of 7 to move to Room 3. Now the time limit is 8.
• He consumes a time of 5 to move to Room 4. Now the time limit is 3.

Sample Input 2

4 1 10
10 7 5
2 10

Sample Output 2

No

He cannot move from Room 1 to Room 2.

Problem Statement

There are N platforms arranged in a row. The height of the i-th platform from the left is H_i.

Takahashi is initially standing on the leftmost platform.

Since he likes heights, he will repeat the following move as long as possible.

• If the platform he is standing on is not the rightmost one, and the next platform to the right has a height greater than that of the current platform, step onto the next platform.

Find the height of the final platform he will stand on.

Constraints

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

Sample Input 1

5
1 5 10 4 2

Sample Output 1

10

Takahashi is initially standing on the leftmost platform, whose height is 1. The next platform to the right has a height of 5 and is higher than the current platform, so he steps onto it.

He is now standing on the 2-nd platform from the left, whose height is 5. The next platform to the right has a height of 10 and is higher than the current platform, so he steps onto it.

He is now standing on the 3-rd platform from the left, whose height is 10. The next platform to the right has a height of 4 and is lower than the current platform, so he stops moving.

Thus, the height of the final platform Takahashi will stand on is 10.

Sample Input 2

3
100 1000 100000

Sample Output 2

100000

Sample Input 3

4
27 1828 1828 9242

Sample Output 3

1828

Problem Statement

For two strings A and B, let A+B denote the concatenation of A and B in this order.

You are given N strings S_1,\ldots,S_N. Modify and print them as follows, in the order i=1, \ldots, N:

• if none of S_1,\ldots,S_{i-1} is equal to S_i, print S_i;
• if X (X>0) of S_1,\ldots,S_{i-1} are equal to S_i, print S_i+ ( +X+ ), treating X as a string.

Constraints

• 1 \leq N \leq 2\times 10^5
• S_i is a string of length between 1 and 10 (inclusive) consisting of lowercase English letters.

Sample Input 1

5
newfile
newfile
newfolder
newfile
newfolder

Sample Output 1

newfile
newfile(1)
newfolder
newfile(2)
newfolder(1)

Sample Input 2

11
a
a
a
a
a
a
a
a
a
a
a

Sample Output 2

a
a(1)
a(2)
a(3)
a(4)
a(5)
a(6)
a(7)
a(8)
a(9)
a(10)

Problem Statement

You are given patterns S and T consisting of # and ., each with H rows and W columns.
The pattern S is given as H strings, and the j-th character of S_i represents the element at the i-th row and j-th column. The same goes for T.

Determine whether S can be made equal to T by rearranging the columns of S.

Here, rearranging the columns of a pattern X is done as follows.

• Choose a permutation P=(P_1,P_2,\dots,P_W) of (1,2,\dots,W).
• Then, for every integer i such that 1 \le i \le H, simultaneously do the following.
  • For every integer j such that 1 \le j \le W, simultaneously replace the element at the i-th row and j-th column of X with the element at the i-th row and P_j-th column.

Constraints

• H and W are integers.
• 1 \le H,W
• 1 \le H \times W \le 4 \times 10^5
• S_i and T_i are strings of length W consisting of # and ..

Sample Input 1

3 4
##.#
##..
#...
.###
..##
...#

Sample Output 1

Yes

If you, for instance, arrange the 3-rd, 4-th, 2-nd, and 1-st columns of S in this order from left to right, S will be equal to T.

Sample Input 2

3 3
#.#
.#.
#.#
##.
##.
.#.

Sample Output 2

No

In this input, S cannot be made equal to T.

Sample Input 3

2 1
#
.
#
.

Sample Output 3

Yes

It is possible that S=T.

Sample Input 4

8 7
#..#..#
.##.##.
#..#..#
.##.##.
#..#..#
.##.##.
#..#..#
.##.##.
....###
####...
....###
####...
....###
####...
....###
####...

Sample Output 4

Yes

Problem Statement

You are given an integer sequence A = (A_1, \dots, A_N) of length N.

Find the number of triplets of integers (i, j, k) satisfying all of the conditions below.

• 1 \leq i, j, k \leq N
• \frac{A_i}{A_j} = A_k

Constraints

• 1 \leq N \leq 2 \times 10^5
• 1 \leq A_i \leq 2 \times 10^5 \, (1 \leq i \leq N)
• All values in input are integers.

Sample Input 1

3
6 2 3

Sample Output 1

2

(i, j, k) = (1, 2, 3), (1, 3, 2) satisfy the conditions.

Sample Input 2

1
2

Sample Output 2

0

Sample Input 3

10
1 3 2 4 6 8 2 2 3 7

Sample Output 3

62