A string s of length n (1 ≤ n ≤ 26) is called alphabetical if it can be obtained using the following algorithm:

  * first, write an empty string to s (i.e. perform the assignment s := ""); 
  * then perform the next step n times; 
  * at the i-th step take i-th lowercase letter of the Latin alphabet and write it either to the left of the string s or to the right of the string s (i.e. perform the assignment s := c+s or s := s+c, where c is the i-th letter of the Latin alphabet). 



In other words, iterate over the n first letters of the Latin alphabet starting from 'a' and etc. Each time we prepend a letter to the left of the string s or append a letter to the right of the string s. Strings that can be obtained in that way are alphabetical.

For example, the following strings are alphabetical: "a", "ba", "ab", "bac" and "ihfcbadeg". The following strings are not alphabetical: "z", "aa", "ca", "acb", "xyz" and "ddcba".

From the given string, determine if it is alphabetical.

Input

The first line contains one integer t (1 ≤ t ≤ 10^4) — the number of test cases. Then t test cases follow.

Each test case is written on a separate line that contains one string s. String s consists of lowercase letters of the Latin alphabet and has a length between 1 and 26, inclusive.

Output

Output t lines, each of them must contain the answer to the corresponding test case. Output YES if the given string s is alphabetical and NO otherwise.

You can output YES and NO in any case (for example, strings yEs, yes, Yes and YES will be recognized as a positive answer).

Example

Input


11
a
ba
ab
bac
ihfcbadeg
z
aa
ca
acb
xyz
ddcba


Output


YES
YES
YES
YES
YES
NO
NO
NO
NO
NO
NO

Note

The example contains test cases from the main part of the condition.
#include <iostream>
#include <stdio.h>
#include <vector>
#include <algorithm>
#include <queue>
#include <map>
#include <string>
#include <string.h>
#define INT_MAX 1987654321
typedef long long int ll;
using namespace std;

int main() {
	ios::sync_with_stdio(false);
	cin.tie(NULL);
	int test; scanf("%d", &test);
	string str;
	bool isa, ans;
	while (test--) {
		cin >> str;
		bool isalpha[30] = { false };
		isa = false;
		ans = true;
		for (int i = 0; i < str.length(); i++) {
			isalpha[str[i] - 'a'] = true;
		}
		for (int i = 0; i < str.length(); i++) {
			if (!isalpha[i]) {
				ans = false;
				break;
			}
		}
		if (ans) {
			for (int i = 0; i < str.length() - 1; i++) {
				if (!isa && str[i] == 'a') isa = true;
				else if (!isa) {
					if (str[i] <= str[i + 1]) {
						ans = false;
						break;
					}
				}
				else {
					if (str[i] >= str[i + 1]) {
						ans = false;
						break;
					}
				}
			}
		}
		if (ans) cout << "YES" << '\n';
		else cout << "NO" << '\n';
	}
	return 0;
}