Problem Statement

Takahashi is a martial artist. There are N moves that a martial artist can learn, called Move 1, 2, \ldots, N. For each 1 \leq i \leq N, it takes T_i minutes of practice to learn Move i. Additionally, at the beginning of that practice, all of the Moves A_{i,1}, A_{i,2}, \ldots, A_{i,K_i} must be already learned. Here, it is guaranteed that A_{i,j} < i for each 1 \leq j \leq K_i.

Takahashi has not learned any move at time 0. He cannot practice for more than one move simultaneously, nor can he stop a practice he has already started. Find the minimum number of minutes needed for Takahashi to learn Move N.

Constraints

• 1 \leq N \leq 2\times 10^5
• 1 \leq T_i \leq 10^9
• 0 \leq K_i < i
• 1 \leq A_{i,j} < i
• \sum_{i=1}^N K_i \leq 2\times 10^5
• A_{i,1}, A_{i,2}, \ldots, A_{i,K_i} are all distinct.
• All values in input are integers.

Sample Input 1

3
3 0
5 1 1
7 1 1

Sample Output 1

10

Here is one possible plan for Takahashi.

• At time 0, start practicing for Move 1 to learn Move 1 at time 3.
• Then, at time 3, start practicing for Move 3 to learn Move 3 at time 10.

Here, Takahashi spends 3+7=10 minutes to learn Move 3, which is the fastest possible. Note that he does not need to learn Move 2 to learn Move 3.

Sample Input 2

5
1000000000 0
1000000000 0
1000000000 0
1000000000 0
1000000000 4 1 2 3 4

Sample Output 2

5000000000

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

Problem Statement

You are given a sequence A=(A_1,\ldots,A_N) of length N.

For each i=1,\ldots,N, solve the following problem.

Problem: Find the sum of all elements in A that are greater than A_i.

Constraints

• 1 \leq N \leq 2\times 10^5
• 1 \leq A_i \leq 10^6
• All input values are integers.

Sample Input 1

5
1 4 1 4 2

Sample Output 1

10 0 10 0 8

• For i=1, the sum of elements greater than A_1=1 is 4+4+2=10.
• For i=2, the sum of elements greater than A_2=4 is 0.
• For i=3, the sum of elements greater than A_3=1 is 4+4+2=10.
• For i=4, the sum of elements greater than A_4=4 is 0.
• For i=5, the sum of elements greater than A_5=2 is 4+4=8.

Sample Input 2

10
31 42 59 26 53 58 97 93 23 54

Sample Output 2

456 414 190 487 361 249 0 97 513 307

Sample Input 3

50
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

Sample Output 3

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

Problem Statement

You are given a positive integer N. It is known that N can be represented as N=p^2q using two different prime numbers p and q.

Find p and q.

You have T test cases to solve.

Constraints

• All values in the input are integers.
• 1\leq T\leq 10
• 1\leq N \leq 9\times 10^{18}
• N can be represented as N=p^2q using two different prime numbers p and q.

Sample Input 1

3
2023
63
1059872604593911

Sample Output 1

17 7
3 7
104149 97711

For the first test case, we have N=2023=17^2\times 7. Thus, p=17 and q=7.

Problem Statement

You have a grid with H rows from top to bottom and W columns from left to right. We denote by (i, j) the square at the i-th row from the top and j-th column from the left. (i,j)\ (1\leq i\leq H,1\leq j\leq W) has an integer A _ {i,j} between 1 and N written on it.

You are given integers h and w. For all pairs (k,l) such that 0\leq k\leq H-h and 0\leq l\leq W-w, solve the following problem:

• If you black out the squares (i,j) such that k\lt i\leq k+h and l\lt j\leq l+w, how many distinct integers are written on the squares that are not blacked out?

Note, however, that you do not actually black out the squares (that is, the problems are independent).

Constraints

• 1 \leq H,W,N \leq 300
• 1 \leq h \leq H
• 1 \leq w \leq W
• (h,w)\neq(H,W)
• 1 \leq A _ {i,j} \leq N\ (1\leq i\leq H,1\leq j\leq W)
• All values in the input are integers.

Sample Input 1

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

Sample Output 1

4 4 3
5 3 4

The given grid is as follows:

For example, when (k,l)=(0,0), four distinct integers 1,3,4, and 5 are written on the squares that are not blacked out, so 4 is the answer.

Sample Input 2

5 6 9 3 4
7 1 5 3 9 5
4 5 4 5 1 2
6 1 6 2 9 7
4 7 1 5 8 8
3 4 3 3 5 3

Sample Output 2

8 8 7
8 9 7
8 9 8

Sample Input 3

9 12 30 4 7
2 2 2 2 2 2 2 2 2 2 2 2
2 2 20 20 2 2 5 9 10 9 9 23
2 29 29 29 29 29 28 28 26 26 26 15
2 29 29 29 29 29 25 25 26 26 26 15
2 29 29 29 29 29 25 25 8 25 15 15
2 18 18 18 18 1 27 27 25 25 16 16
2 19 22 1 1 1 7 3 7 7 7 7
2 19 22 22 6 6 21 21 21 7 7 7
2 19 22 22 22 22 21 21 21 24 24 24

Sample Output 3

21 20 19 20 18 17
20 19 18 19 17 15
21 19 20 19 18 16
21 19 19 18 19 18
20 18 18 18 19 18
18 16 17 18 19 17

Problem Statement

Let the similarity f(X,Y) between two strings X and Y be the length of their longest common prefix.
For example, the similarity between abc and axbc is 1, and the similarity between aaa and aaaa is 3.

You are given a string S of length N. Let S_i be the suffix of S beginning with the i-th character of S. For each k=1,\ldots,N, find f(S_k,S_1)+f(S_k,S_2)+\ldots+f(S_k,S_N).

Constraints

• 1 \leq N \leq 10^6
• S is a string of length N consisting of lowercase English letters.

Sample Input 1

3
abb

Sample Output 1

3
3
2

S_1 is abb, S_2 is bb, and S_3 is b.

• For k=1: f(S_1,S_1)+f(S_1,S_2)+f(S_1,S_3)=3+0+0=3.
• For k=2: f(S_2,S_1)+f(S_2,S_2)+f(S_2,S_3)=0+2+1=3.
• For k=3: f(S_3,S_1)+f(S_3,S_2)+f(S_3,S_3)=0+1+1=2.

Sample Input 2

11
mississippi

Sample Output 2

11
16
14
12
13
11
9
7
4
3
4