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

There is a grid with H rows from top to bottom and W columns from left to right. Let (i, j) denote the square at the i-th row from the top and j-th column from the left.
The squares are described by characters C_{i,j}. If C_{i,j} is ., (i, j) is empty; if it is #, (i, j) contains a box.

For integers j satisfying 1 \leq j \leq W, let the integer X_j defined as follows.

• X_j is the number of boxes in the j-th column. In other words, X_j is the number of integers i such that C_{i,j} is #.

Find all of X_1, X_2, \dots, X_W.

Constraints

• 1 \leq H \leq 1000
• 1 \leq W \leq 1000
• H and W are integers.
• C_{i, j} is . or #.

Sample Input 1

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

Sample Output 1

1 2 0 3

In the 1-st column, one square, (1, 1), contains a box. Thus, X_1 = 1.
In the 2-nd column, two squares, (2, 2) and (3, 2), contain a box. Thus, X_2 = 2.
In the 3-rd column, no squares contain a box. Thus, X_3 = 0.
In the 4-th column, three squares, (1, 4), (2, 4), and (3, 4), contain a box. Thus, X_4 = 3.
Therefore, the answer is (X_1, X_2, X_3, X_4) = (1, 2, 0, 3).

Sample Input 2

3 7
.......
.......
.......

Sample Output 2

0 0 0 0 0 0 0

There may be no square that contains a box.

Sample Input 3

8 3
.#.
###
.#.
.#.
.##
..#
##.
.##

Sample Output 3

2 7 4

Sample Input 4

5 47
.#..#..#####..#...#..#####..#...#...###...#####
.#.#...#.......#.#...#......##..#..#...#..#....
.##....#####....#....#####..#.#.#..#......#####
.#.#...#........#....#......#..##..#...#..#....
.#..#..#####....#....#####..#...#...###...#####

Sample Output 4

0 5 1 2 2 0 0 5 3 3 3 3 0 0 1 1 3 1 1 0 0 5 3 3 3 3 0 0 5 1 1 1 5 0 0 3 2 2 2 2 0 0 5 3 3 3 3

Problem Statement

There are N sellers and M buyers in an apple market.

The i-th seller may sell an apple for A_i yen or more (yen is the currency in Japan).

The i-th buyer may buy an apple for B_i yen or less.

Find the minimum integer X that satisfies the following condition.

Condition: The number of people who may sell an apple for X yen is greater than or equal to the number of people who may buy an apple for X yen.

Constraints

• 1 \leq N,M \leq 2\times 10^5
• 1\leq A_i,B_i \leq 10^9
• All input values are integers.

Sample Input 1

3 4
110 90 120
100 80 120 10000

Sample Output 1

110

Two sellers, the 1-st and 2-nd, may sell an apple for 110 yen; two buyers, the 3-rd and 4-th, may buy an apple for 110 yen. Thus, 110 satisfies the condition.

Since an integer less than 110 does not satisfy the condition, this is the answer.

Sample Input 2

5 2
100000 100000 100000 100000 100000
100 200

Sample Output 2

201

Sample Input 3

3 2
100 100 100
80 120

Sample Output 3

100

Problem Statement

You are given a string S of length N consisting of lowercase English letters, ,, and ". It is guaranteed that S contains an even number of ".

Let 2K be the number of " in S. For each i=1,2,\ldots,K, the characters from the (2i-1)-th " through the (2i)-th " are said to be enclosed.

Your task is to replace each , in S that is not an enclosed character with . and print the resulting string.

Constraints

• N is an integer between 1 and 2\times 10^5, inclusive.
• S is a string of length N consisting of lowercase English letters, ,, and ".
• S contains an even number of ".

Sample Input 1

8
"a,b"c,d

Sample Output 1

"a,b"c.d

In S, "a,b" are enclosed characters, and c,d are not.

The , in S that is not an enclosed character is the seventh character from the left in S, so replace that character with . to get the answer.

Sample Input 2

5
,,,,,

Sample Output 2

.....

Sample Input 3

20
a,"t,"c,"o,"d,"e,"r,

Sample Output 3

a."t,"c."o,"d."e,"r.

Problem Statement

You are given positive integers N and M.
Find the smallest positive integer X that satisfies both of the conditions below, or print -1 if there is no such integer.

• X can be represented as the product of two integers a and b between 1 and N, inclusive. Here, a and b may be the same.
• X is at least M.

Constraints

• 1\leq N\leq 10^{12}
• 1\leq M\leq 10^{12}
• N and M are integers.

Sample Input 1

5 7

Sample Output 1

8

First, 7 cannot be represented as the product of two integers between 1 and 5.
Second, 8 can be represented as the product of two integers between 1 and 5, such as 8=2\times 4.

Thus, you should print 8.

Sample Input 2

2 5

Sample Output 2

-1

Since 1\times 1=1, 1\times 2=2, 2\times 1=2, and 2\times 2=4, only 1, 2, and 4 can be represented as the product of two integers between 1 and 2, so no number greater than or equal to 5 can be represented as the product of two such integers.
Thus, you should print -1.

Sample Input 3

100000 10000000000

Sample Output 3

10000000000

For a=b=100000 (=10^5), the product of a and b is 10000000000 (=10^{10}), which is the answer.
Note that the answer may not fit into a 32-bit integer type.