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.*;

public class Main {
    public static void main(String args[]) {
        Scanner s = new Scanner(System.in);
        int t = s.nextInt();
        while(t-->0){
            solve(s);
        }
    }

    static void solve(Scanner sc){
        String s = sc.next();
        // System.out.println(s);
        for(int i=0;i<s.length();i++){
            char ch = s.charAt(i);
            int count = 0;
            for(int j=i+1;j<s.length();j++){
                if(s.charAt(j)<ch)count++;
                else if(s.charAt(i)==s.charAt(j)){
                    System.out.println("NO");
                    return;
                }
            }

            if(count==ch-'a')continue;
            count = 0;
            for(int j=0;j<i;j++){
                if(s.charAt(j)<ch)count++;
                else if(s.charAt(i)==s.charAt(j)){
                    System.out.println("NO");
                    return;
                }
            }

            if(count!=ch-'a'){
                System.out.println("NO");
                return;
            }

            
        }
        System.out.println("YES");
    }
}