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.PrintWriter;
import java.util.Scanner;

public class Main {

    static Scanner sc = new Scanner(System.in);
    static PrintWriter out = new PrintWriter(System.out);

    public static void main(String[] args) {
        int cases = sc.nextInt();
        sc.nextLine();
        for (int i = 0; i < cases; i++) {
            boolean result = isAlphabetical(sc.nextLine());
            out.println(result ? "YES" : "NO");
        }
        out.close();
    }

    private static boolean isAlphabetical(String string) {
        if (string.length() == 1 && string.charAt(0) != 'a') return false;
        int left = 0;
        int right = string.length() - 1;
        char max = (char) ('a' + right);
        while (left < right) {
            char lc = string.charAt(left);
            char llc = string.charAt(left + 1);
            char rc = string.charAt(right);
            char rrc = string.charAt(right - 1);
            if (lc == max) {
                left ++;
                if (lc == rc +1) {
                    max = rc;
                    continue;
                } else if (lc == llc + 1) {
                    max = llc;
                    continue;
                }
            } else if (rc == max) {
                right --;
                if (lc + 1 == rc) {
                    max = lc;
                    continue;
                } else if (rrc + 1 == rc) {
                    max = rrc;
                    continue;
                }
            }
            return false;
        }
        return true;
    }
}
