C. Equal Frequencies
time limit per test
2 seconds
memory limit per test
512 megabytes
input
standard input
output
standard output

Let's call a string balanced if all characters that are present in it appear the same number of times. For example, "coder", "appall", and "ttttttt" are balanced, while "wowwow" and "codeforces" are not.

You are given a string $$$s$$$ of length $$$n$$$ consisting of lowercase English letters. Find a balanced string $$$t$$$ of the same length $$$n$$$ consisting of lowercase English letters that is different from the string $$$s$$$ in as few positions as possible. In other words, the number of indices $$$i$$$ such that $$$s_i \ne t_i$$$ should be as small as possible.

Input

Each test contains multiple test cases. The first line contains the number of test cases $$$t$$$ ($$$1 \le t \le 10^4$$$). The description of the test cases follows.

Each test case consists of two lines. The first line contains a single integer $$$n$$$ ($$$1 \le n \le 10^5$$$) — the length of the string $$$s$$$.

The second line contains the string $$$s$$$ of length $$$n$$$ consisting of lowercase English letters.

It is guaranteed that the sum of $$$n$$$ over all test cases does not exceed $$$10^5$$$.

Output

For each test case, print the smallest number of positions where string $$$s$$$ and a balanced string $$$t$$$ can differ, followed by such a string $$$t$$$.

If there are multiple solutions, print any. It can be shown that at least one balanced string always exists.

Example
Input
4
5
hello
10
codeforces
5
eevee
6
appall
Output
1
helno
2
codefofced
1
eeeee
0
appall
Note

In the first test case, the given string "hello" is not balanced: letters 'h', 'e', and 'o' appear in it once, while letter 'l' appears twice. On the other hand, string "helno" is balanced: five distinct letters are present in it, and each of them appears exactly once. Strings "hello" and "helno" differ in just one position: the fourth character. Other solutions are possible too.

In the second test case, string "codefofced" is balanced since only letters 'c', 'o', 'd', 'e', and 'f' are present in it, and each of them appears exactly twice.

In the third test case, string "eeeee" is balanced since only letter 'e' is present in it.

In the fourth test case, the given string "appall" is already balanced.