Vasya came up with a password to register for EatForces — a string . The password in EatForces should be a string, consisting of lowercase and uppercase Latin letters and digits.
But since EatForces takes care of the security of its users, user passwords must contain at least one digit, at least one uppercase Latin letter and at least one lowercase Latin letter. For example, the passwords
3R24m are valid, and the passwords
Password are not.
A substring of string is a string . is the length of the substring. Note that the empty string is also considered a substring of , it has the length .
Vasya's password, however, may come too weak for the security settings of EatForces. He likes his password, so he wants to replace some its substring with another string of the same length in order to satisfy the above conditions. This operation should be performed exactly once, and the chosen string should have the minimal possible length.
Note that the length of should not change after the replacement of the substring, and the string itself should contain only lowercase and uppercase Latin letters and digits.
The first line contains a single integer ( ) — the number of testcases.
Each of the next lines contains the initial password s ( ) , consisting of lowercase and uppercase Latin letters and digits.
Only is allowed for hacks.
For each testcase print a renewed password, which corresponds to given conditions.
The length of the replaced substring is calculated as following: write down all the changed positions. If there are none, then the length is . Otherwise the length is the difference between the first and the last changed position plus one. For example, the length of the changed substring between the passwords
a7cdEf is , because the changed positions are and , thus .
It is guaranteed that such a password always exists.
If there are several suitable passwords — output any of them.
In the first example Vasya's password lacks a digit, he replaces substring
C with and gets password
abcD4E. That means, he changed the substring of length .
In the second example Vasya's password is ok from the beginning, and nothing has to be changed. That is the same as replacing the empty substring with another empty substring (length ).
You are given a set of all integers from to inclusive, , and is always odd.
You want to split these numbers into exactly pairs in such a way that for each pair the greatest common divisor of and is equal to . Each number should appear in exactly one of the pairs.
Print the resulting pairs or output that no solution exists. If there are multiple solutions, print any of them.
The only line contains two integers and ( , is odd).
If any solution exists, print "YES" in the first line. Each of the next lines should contain some pair of integers. GCD of numbers in each pair should be equal to . All numbers should be pairwise distinct and should have values from to inclusive.
If there are multiple solutions, print any of them.
If there exists no solution, print