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.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;

public class AlphabeticalStrings {
    public static void main(String[] args) throws IOException {
        BufferedReader in = new BufferedReader(new InputStreamReader(System.in));
        int t = Integer.parseInt(in.readLine());
        for(int a = 0; a < t; a++)
        {
            String s = in.readLine();
            int apos = 100;
            if (s.contains("a"))
            {
                if (s.length() == 1) {
                    System.out.println("YES");
                    continue;
                }

                char [] sarr = s.toCharArray();
                apos = s.indexOf('a');
                int left = apos, right = apos, itr = 1;

                for (char ch = 'b'; ch <= 'z'; ch++) {
                    if ( left >= 1 && sarr[left - 1] == ch) {
                        left -=  1;
                    }
                    else if ( right != s.length() - 1 && (right <= s.length() - 1) && sarr[right + 1] == ch) {
                        right += 1;
                    } else {
                        System.out.println("NO");
                        break;
                    }

                    if (left == 0 && right == s.length() - 1) {
                        System.out.println("YES");
                        break;
                    }
                }
            } else {
                System.out.println("NO");
            }
        }

    }
}
