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;
typedef long long int lli;
int main()
{
       lli t;
       cin>>t;
       while(t--)
       {
              string s;
              cin>>s;
              map<char,lli> m1;
             
            for(lli i=0;i<s.length();i++)
            {
                   m1[s[i]]++;
            }
            lli flag=0;
            lli prev=0;
             for(auto e:m1)
             {
                   char ch=e.first;
                   if(m1[ch]>1)
                   {
                          cout<<"No"<<endl;
                          flag=1;
                          break;
                   }
                   else if((ch-'a'+1)-prev!=1)
                   {
                          cout<<"NO"<<endl;
                          flag=1;
                          break;
                   }
                   prev=ch-'a'+1;
             }
             if(flag==0)
             {
             lli i;
             for( i=0;s[i]!='a';i++)
             {
                    if(s[i]<=s[i+1])
                    {
                           cout<<"no"<<endl;
                           flag=1;
                           break;
                    }
             }
             if(flag==0)
             {
             for(lli j=i;j<s.length()-1;j++)
             {
                    if(s[j]>=s[j+1])
                    {
                           cout<<"no"<<endl;
                           flag=1;
                           break;
                    }
             }
             }
             if(flag==0)
             {
                    cout<<"yes"<<endl;
             }
             }
       }
}
                    
               