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 int
#define loop(i,n,a) for(int i=a;i<n;i++)
using namespace std;
void solve()
{
    string s;
    cin>>s;
    int n=s.size();
    int i=0;
    bool flag=false;
    for(char x:s){
        if(x=='a'){
            flag=true;
            break;
        }
        i++;
    }
    if(n==1 && flag)n--;
    int size=1,pos=1;
    while(n-- && flag){
         if(n==1){
            if(pos){
                 if(i+1<s.size() && (int)s[i+1]==(int)'a'+size){
                 pos=1;
                 i++;
                }
                else if(i-size>=0 && (int)s[i-size]==(int)'a'+size){
                         pos=0;
                         i-=size;
                }
                else flag=false;
            }
            else{
                if(i-1>=0 && (int)s[i-1]==(int)'a'+size){
                    pos=0;
                    i--;
                }
                else if(i+size<s.size() && (int)s[i+size]==(int)'a'+size){
                    pos=1;
                    i+=size;
                }
                else flag=false;
                }
             break;
        }
        else{
             if(pos)
        {
            if(i+1<s.size() && (int)s[i+1]==(int)'a'+size){
                pos=1;
                i++;
            }
            else if(i-size>=0 && (int)s[i-size]==(int)'a'+size){
                pos=0;
                i-=size;
            }
            else flag=false;
        }
        else if(n>1){
            if(i-1>=0 && (int)s[i-1]==(int)'a'+size){
                pos=0;
                i--;
            }
            else if(i+size<s.size() && (int)s[i+size]==(int)'a'+size){
                pos=1;
                i+=size;
            }
            else flag=false;
        }
        if(!flag)break;
                    size++;
        }
    }
    if(flag)printf("Yes\n");
    else printf("No\n");
}
int main()
{
    int T;
    cin>>T;
    while(T>0)
    {
        solve();
        T--;
    }
}