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;
bool check(string s)
{  int n=s.length();
       map<int,int> mp;
       for(int i=0;i<n;i++)
       {
              mp[s[i]-'a']++;
       }
       for(int i=0;i<n;i++)
       {
              if(mp[i]!=1)
              {
                     return false;
              }
       }
       return true;
}
bool check2(string s)
{  int n=s.length();
       int flag=0;
       int i=0;
       for( i=0;i<n;i++)
       {   if(s[i]=='a')
       {   
              break;
       }
         else if(s[i+1]>s[i])
          {
                 return false;
          }
       }
       for(int j=i;j<n-1;j++)
       {   
              if(s[j+1]<s[j])
              {
                     return false;
              }
       }
       return true;
}
int main()
{
       int t;
       cin>>t;
       while(t--)
       {
              string s;
              cin>>s;
             bool p= check(s);
             if(p)
             {
                   if(check2(s))
                   {cout<<"yes"<<endl;
                          
                   }
                   else{
                          cout<<"no"<<endl;
                   }
             }
             else{
                    cout<<"no"<<endl;
             }
       }
}