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.
#include <bits/stdc++.h>
using namespace std;

void solve(){
	string str;
	int t=-1,l,r,n;
	char ch='b',ch2='a';
	cin>>str;
	n=str.size();
	if(n==1&&str[0]=='a'){
		cout<<"YES\n";
		return;
	}
	else if(n==1&&str[0]!='a'){
		cout<<"NO\n";
		return;
	}
	ch2+=n-1;
	for(int i=0;i<(int)str.size();i++){
		if(str[i]=='a'){
			t=i;
			break;
		}
	}
	if(t==-1){
		cout<<"NO\n";
	}
	else{
		l=t-1;
		r=t+1;
		while(1){
			if(l>=0&&str[l]==ch) {
				if(ch==ch2) break;
				ch++;
				l--;
			}
			else if(r<n&&str[r]==ch) {
				if(ch==ch2) break;
				ch++;
				r++;
			}
			else{
				cout<<"NO\n";
				return;
			}
		}
		cout<<"YES\n";
	}
}




int main(){
	ios::sync_with_stdio(0);
	cin.tie(0);cout.tie(0);
	int t;
	cin>>t;
	while(t--){
		solve();
	}
	return 0;
}
