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 AlphabeticalStrings {
    public static void main(String[] args) {
        Scanner a = new Scanner(System.in);
        int test = a.nextInt() ;
        a.nextLine();
        for (int b = 0 ; b < test ; b++ ){
            int cur = 98 ;
            String s = a.nextLine();
            int start = s.indexOf('a');
            if (start == -1) System.out.println("No");
            else if (s.length() == 1 )
                System.out.println(start==0?"Yes":"No");
            else {
            boolean alp = true ;
            int end = start+1 ;
            start--;
            while(start >= 0 || end < s.length()){
                if ( start >= 0 &&s.indexOf(cur) == start){
                    cur++;
                    start--;
                }
                else if ( end < s.length() && s.indexOf(cur) == end){
                    cur++;
                    end++;
                }
                else {
                    alp = false;
                    break;
                }
            }
            System.out.println(alp?"Yes":"No");
            }
        }
    }
}
