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.HashMap;
import java.util.HashSet;
import java.util.Scanner;

public class Alphabetical {
    static HashMap<String, Integer> map = new HashMap<String, Integer>();
    static HashSet<String> set = new HashSet<String>();

    public static void main(String[] args) {
        int index = 1;
        for (char ch = 'a'; ch <= 'z'; ++ch) {
            map.put(String.valueOf(ch), index);
            index++;
        }
        Scanner scan = new Scanner(System.in);
        int n = scan.nextInt();
        for (int i = 0; i < n; i++) {
            String s = scan.next();
            if (alphabetic(s))
                System.out.println("YES");
            else
                System.out.println("NO");
        }
    }

    public static boolean alphabetic(String s) {
        int n = s.length();
        int[] count = new int[26];
        for (int i = 0; i < n; i++) {
            count[s.charAt(i) - 'a']++;
        }
        for (int i = 0; i < count.length; i++) {
            if (count[i] > 1)
                return false;
            if (i > n && count[i] > 0)
                return false;
            if (i < n && count[i] == 0)
                return false;
        }
        int[] arr = new int[s.length()];
        String ch = "";
        int aindex = 0;
        for (int i = 0; i < s.length(); i++) {
            ch = s.charAt(i) + "";
            arr[i] = map.get(ch);
            if (arr[i] == 1)
                aindex = i;
        }
        for (int i = 0; i < aindex; i++) {
            if (arr[i] < arr[i + 1])
                return false;
        }
        for (int i = aindex; i < arr.length - 1; i++) {
            if (arr[i] > arr[i + 1])
                return false;
        }
        return true;
    }
}
