Problem Statement

In this problem, an input file contains multiple test cases.
You are first given an integer T. Solve the following problem for T test cases.

• We have N positive integers A_1, A_2, ..., A_N. How many of them are odd?

Constraints

• 1 \leq T \leq 100
• 1 \leq N \leq 100
• 1 \leq A_i \leq 10^9
• All values in the input are integers.

Sample Input 1

4
3
1 2 3
2
20 23
10
6 10 4 1 5 9 8 6 5 1
1
1000000000

Sample Output 1

2
1
5
0

This input contains four test cases.

The second and third lines correspond to the first test case, where N = 3, A_1 = 1, A_2 = 2, A_3 = 3.
We have two odd numbers in A_1, A_2, and A_3, so the first line should contain 2.

Problem Statement

You are given a string S consisting of lowercase English letters. How many different non-empty substrings does S have?

A substring is a contiguous subsequence. For example, xxx is a substring of yxxxy but not of xxyxx.

Constraints

• S is a string of length between 1 and 100, inclusive, consisting of lowercase English letters.

Sample Input 1

yay

Sample Output 1

5

S has the following five different non-empty substrings:

• a
• y
• ay
• ya
• yay

Sample Input 2

aababc

Sample Output 2

17

Sample Input 3

abracadabra

Sample Output 3

54

Problem Statement

Planning to place many PCs in his room, Takahashi has decided to write a code that finds how many PCs he can place in his room.

You are given H strings S_1,S_2,\ldots,S_H, each of length W, consisting of . and T.

Takahashi may perform the following operation any number of times (possibly zero):

• Choose integers satisfying 1\leq i \leq H and 1 \leq j \leq W-1 such that the j-th and (j+1)-th characters of S_i are both T. Replace the j-th character of S_i with P, and (j+1)-th with C.

He tries to maximize the number of times he performs the operation. Find possible resulting S_1,S_2,\ldots,S_H.

Constraints

• 1\leq H \leq 100
• 2\leq W \leq 100
• H and W are integers.
• S_i is a string of length W consisting of . and T.

Sample Input 1

2 3
TTT
T.T

Sample Output 1

PCT
T.T

He can perform the operation at most once.

For example, an operation with (i,j)=(1,1) makes S_1 PCT.

Sample Input 2

3 5
TTT..
.TTT.
TTTTT

Sample Output 2

PCT..
.PCT.
PCTPC

Problem Statement

For a non-negative integer K, we define a level-K carpet as follows:

• A level-0 carpet is a 1 \times 1 grid consisting of a single black cell.
• For K > 0, a level-K carpet is a 3^K \times 3^K grid. When this grid is divided into nine 3^{K-1} \times 3^{K-1} blocks:
  • The central block consists entirely of white cells.
  • The other eight blocks are level-(K-1) carpets.

You are given a non-negative integer N.
Print a level-N carpet according to the specified format.

Constraints

• 0 \leq N \leq 6
• N is an integer.

Sample Input 1

1

Sample Output 1

###
#.#
###

A level-1 carpet is a 3 \times 3 grid as follows:

When output according to the specified format, it looks like the sample output.

Sample Input 2

2

Sample Output 2

#########
#.##.##.#
#########
###...###
#.#...#.#
###...###
#########
#.##.##.#
#########

A level-2 carpet is a 9 \times 9 grid.

Problem Statement

In a town divided into a grid with N rows and 10^9 columns, there are N walls, numbered 1 to N.
Wall i ranges from the L_i-th column to the R_i-th column from the left in the i-th row from the top. (See also the figure at Sample Input and Output 1.)

Takahashi has decided to destroy all N walls.
With his superhuman strength, his one punch can damage consecutive D columns at once.

• More formally, he can choose an integer x between 1 and 10^9 - D + 1 (inclusive) to damage all walls that exist (or partly exist) in the x-th through (x + D - 1)-th columns and are not yet destroyed.

When a part of a wall is damaged, that whole wall will be destroyed by the impact of the punch.
(See also the figure at Sample Input and Output 1.)

At least how many times does Takahashi need to punch to destroy all walls?

Constraints

• 1 \leq N \leq 2 \times 10^5
• 1 \leq D \leq 10^9
• 1 \leq L_i \leq R_i \leq 10^9
• All values in input are integers.

Sample Input 1

3 3
1 2
4 7
5 9

Sample Output 1

2

The figure below describes the arrangements of walls in Sample Input 1.

He can destroy all walls with two punches, such as the following. (Below, \lbrack a, b \rbrack denotes the range from the a-th through b-th columns.)

• First, punch \lbrack 2, 4 \rbrack. The walls existing in \lbrack 2, 4 \rbrack ― Walls 1 and 2 ― are damaged and destroyed.
• Second, punch \lbrack 5, 7 \rbrack. The wall existing in \lbrack 5, 7 \rbrack ― Wall 3 ― is damaged and destroyed.

It is also possible to destroy all walls with two punches in this way:

• First, punch \lbrack 7, 9 \rbrack to destroy Walls 2 and 3.
• Second, punch \lbrack 1, 3 \rbrack to destroy Wall 1.

Sample Input 2

3 3
1 2
4 7
4 9

Sample Output 2

1

The difference from Sample Input/Output 1 is that Wall 3 now covers \lbrack 4, 9 \rbrack, not \lbrack 5, 9 \rbrack.
In this case, he can punch \lbrack 2, 4 \rbrack to destroy all walls with one punch.

Sample Input 3

5 2
1 100
1 1000000000
101 1000
9982 44353
1000000000 1000000000

Sample Output 3

3