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 Main {
    public static void main(String[] args){
        Scanner scanner = new Scanner(System.in);
        int t = scanner.nextInt();
        while(t>0){
            t--;
            String arr = scanner.next();
            if(isStringOK(arr)) System.out.println("YES");
            else System.out.println("NO");
        }
    }

    public static boolean isStringOK(String arr){
        int l = arr.indexOf('a');
        int u = l;
        if(l==-1) return false;
        l--; u++;
        boolean isOk = true;
        char i = 'a';
        for(char j=1;j<arr.length();j++){
            i+=1;
            if(l<arr.length() && l>=0 && arr.charAt(l) == i)l--;
            else if(u<arr.length() && arr.charAt(u) == i) u++;
            else{
                isOk = false;
                break;
            }
        }
        return isOk;
    }
}