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.Scanner;

public class Temp1 {
	
	
	
	public static void main(String[] args) {
		Scanner s = new Scanner(System.in);
		int test = s.nextInt();
		for(int t = 0; t < test; t++) {
			String str = s.next();
			boolean ans = true;
			int length = 0;
			int start = 0;
			int next = 0;
			for(int i = 0; i < str.length(); i++) {
				if(str.charAt(i) == 'a') {
					start = i;
					length++;
					break;
				}
			}
			next = 'a'+1;
			int prev = start - 1;
			int forw = start + 1;
			while(length < str.length()) {
				if(prev > -1) {
					
					if(str.charAt(prev) == next) {
						length++;
						prev--;
						next++;
						continue;
					}
				}
				if(forw < str.length()) {
					if(str.charAt(forw) == next) {
						length++;
						forw++;
						next++;
						continue;
					}
				}
				ans = false;
				break;
			}
			if(ans) {
				System.out.println("YES");
			}else {
				System.out.println("NO");
			}
		}
	}
}