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>
typedef long long int lli;
using namespace std;

void solve(){
    string s;
    cin >> s;
    int pos = -100;
    int n = s.size();
    for (int i = 0; i < n; i++){
        if (s[i] == 'a'){
            pos = i;
        }
    }
    if (pos == -100){
        cout << "NO\n";
        return;
    }
    if (s == "a" || s == "ab" || s == "ba"){
        cout << "YES\n";
        return;
    }
    int i = pos - 1, j = pos + 1;
    char next = 'b';
    while (i >= -1 || j <= n){
        if (i == -1 && j == n){
            break;
        }
        //cout << "next: " << next << " i: " << i << " j: " << j << "\n";
        if (s[i] == next){
            i--;
            next++;
            continue;
        }
        else if (s[j] == next){
            j++;
            next++;
            continue;
        }
        else{
            cout << "NO\n";
            return;
        }
    }
    cout << "YES\n";
}

int main (){
    ios_base::sync_with_stdio(false);
    cin.tie(NULL);
    int t;
    //t = 1;
    cin >> t;
    while (t--){
        solve();
    }
    return 0;
}