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.io.*;
import java.util.*;

public class as {
    public static void main(String[] args) throws IOException {
        BufferedReader in = new BufferedReader(new InputStreamReader(System.in));
        int t = Integer.parseInt(in.readLine());
        for (int i = 0; i < t; i++) {
            boolean ans = true;
            int[] occ = new int[26];
            Arrays.fill(occ, -1);
            String s = in.readLine();
            for (int j = 0; j < s.length(); j++) {
                if (occ[s.charAt(j) - 'a'] != -1) {
                    ans = false;
                    break;
                }
                occ[s.charAt(j) - 'a'] = j;
            }
            boolean end = false;
            int li = occ[0], hi = occ[0];
            if (li == -1) ans = false;
            for (int a = 1; a < 26; a++) {
                if (end && occ[a] != -1) ans = false;
                if (occ[a] == -1) end = true;
                else if (occ[a] == li - 1) li -= 1;
                else if (occ[a] == hi + 1) hi += 1;
                else ans = false;
            }
            if (ans) System.out.println("yes");
            else System.out.println("no");
        }
        in.close();
    }
}