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 <bits/stdc++.h>
#define ll long long
#define EL "\n"
using namespace std;

int Count[50];
string Solve(string s) {
    for (int i = 0; i < 30; i++) Count[i] = 0;
    int P = 0, pos = 0;
    for (int i = 0; i < s.size(); i++) {
        Count[s[i] - 'a']++;
        P = max(P, (int) s[i] - 'a');
        if (s[i] == 'a') pos = i;
    }

    for (int i = 0; i <= P; i++) {
        if (Count[i] != 1) return "NO\n";
    }

    for (int i = 0; i < pos - 1; i++) {
        int x = s[i], y = s[i + 1];
        if (x <= y) return "NO\n";
    }
    for (int i = pos + 1; i < s.size() - 1; i++) {
        int x = s[i], y = s[i + 1];
        if (x >= y) return "NO\n";
    }
    return "YES\n";
}
void Input() {
    ios_base::sync_with_stdio(0);cin.tie(0);cout.tie(0);
    int T; cin >> T;
    while (T--) {
        string s; cin >> s;
        cout << Solve(s);
    }
}

int main() {
    Input();
}
