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.
import java.util.Scanner;

public class alphabeticalStrings {


    public static void main(String[] args) {
Scanner sc= new Scanner(System.in);
int t=sc.nextInt();
        System.out.print(sc.nextLine());
while(t-->0){
   
 String s=sc.nextLine();
 
 if(s.contains("a")){
     int i=s.indexOf("a");
     int j=s.indexOf("a");
     int x=97;                                            //I H F C B A D E G
     int temp=1;
     
     while (temp<s.length()){
         char c=(char)x;
         char d=(char)(x+1);
        if(s.indexOf(d)<0){
            System.out.println("NO");
            break;
        }
         if(s.indexOf(d)<s.indexOf(c)){
          i--;
          x++;
          temp++;
          }
          else{
              j++;
              x++;
              temp++;
          }
         
     if(temp<s.length()){
          char e=(char)(x+1);
          
          if(s.indexOf(e)==i-1 ){
//              i--;
             //temp++;
              continue;
          }
          else if( s.indexOf(e)==j+1){
//              j++;
             // temp++;
              continue;
          }
              else{
              System.out.println("NO");
              break;
              }
     }
       }
     
          if (temp==s.length()){
              System.out.println("YES");
          }
          else{
              continue;
          }
         }
      
 
 else{
     System.out.println("NO");
 }
    
    
}

    }
    
}

