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<iostream>
#include<cmath>
#include<string.h>
using namespace std;
int main()
{
	int t;
	cin>>t;
	while(t--)
	{
		char c[27];
		cin>>c;
		char s=97;
		int pos=-1;
		bool flag=1;
		for(int i=0;i<strlen(c);i++)
		{
			if(c[i]==s)
			{
				pos=i;
				break;
			}
		 } 
		 if(pos==-1) 
		 {
		 	 cout<<"NO"<<endl;
		 	flag=0;
		 }
		 while(strlen(c)!=1)
		{
		 for(int i=pos;i<strlen(c);i++)
		 {
		 	c[i]=c[i+1];
		 }
		 if(c[pos]==(s+1))
		 {
		 	s++;
		 }
		 else if(c[pos-1]==(s+1))
		 {
		 	s++;
		 	pos--;
		 }
		 else
		 {
		 	if(flag) cout<<"NO"<<endl;
		 	flag=0;
		 	break;
		 }
		}
		if(c[0]==s&&flag) cout<<"YES"<<endl;
		else if(flag) cout<<"NO"<<endl;
		
	 } 
}