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> 
using namespace std;

int main() {
 int i,j,k,n,m,t;
 cin>>t;
 while(t--)
 {
    
     string s;
     cin>>s;
     
     for(i=0;i<s.size();i++)
         if(s[i]=='a')
             break;
  //   cout<<i<<endl;
   
       bool flag=false;
     
     
     if(i==s.size())
     flag=true;
     j=i+1;
     i--;
     char ch='b';
   
     while(i>=0 || j<s.size())
     {
       //  cout<<ch<<" ";
         if(i>=0 && s[i]==ch)
         {
         //    cout<<s[i]<<endl;
             i--;
             ch=ch+1;
             
         }
         else if(j<s.size()&& s[j]==ch)
         {
                     //     cout<<s[j]<<endl;

             j++;
             ch=ch+1;
       
             
             
         }
         else
         {
             flag=true;
             break;
             
         }
         
     }
     
     
     if(flag)
         cout<<"NO\n";
     else
         cout<<"YES\n";
         
     
     
     
 }
 
 
 
 
 
 
 
  
}
