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>
#include <iostream>

#define fast                          \
    ios_base::sync_with_stdio(false); \
    cin.tie(0);                       \
    cout.tie(0);

#define ll long long int
#define put push_back 
#define stop return 0
#define vint vector<int>
#define vs vector<string>
#define vll vector<long long int>
#define YES cout<<"YES"<<"\n"
#define NO cout<<"NO"<<"\n"
using namespace std;

int main(){
    fast;
    long long int t=1;
    cin >> t;
    while(t--)
    {
        string s;
        cin >> s;
        int n=s.length();
        if(s.length()==1 && s!="a") NO;
        else if(s.length()==1 && s=="a") YES;
        else if(s.length()==2){
            if(s=="ab" || s=="ba") YES;
            else NO;
        }
        else if(s.length()==3){
            if(s=="abc" || s=="cba" || s=="cab" || s== "bac") YES;
            else NO;
        }
        else{
            set<char> check;
            bool alpha=false;
            for(int i=0;i<s.length();i++){
                check.insert(s[i]);
                if(check.size()==s.length()){
                    int sum=0;
                    for(int i=0;i<check.size();i++) sum+= s[i]-'a'+1;
                    
                    if(sum==(n*(n+1))/2){ alpha=true; break;}
                }


            }
            if(alpha){
            for(int i=1;i<s.length()-1;i++){
                int x= s[i-1]-'a';
                int y= s[i]-'a';
                int z=s[i+1]-'a';
                if(y>x && y>z) {alpha=false; break;}
                
            }
            }
            if(!alpha) NO;
            else YES;

        }

    }
    
    
    stop;
}