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;
int main()
{
	int t;
	cin>>t;
	while(t--)
	{
		string s;
		cin>>s;
		map<char,int>m1,m2;
		vector<int>v(26,0);
		int i,flag=0,x=300,f=0,g=0;
		for(i=0;i<s.size();i++)
		{
			v[s[i]-'a']++;
			if(s[i]=='a')
				flag=1;
			else if(flag==0)
				m1[s[i]]=i;
			else
				m2[s[i]]=i;
		}
		for(i=1;i<26;i++)
		{
			if(v[i]>1||v[i]>v[i-1])
			{
				flag=0;
				break;
			}
		}
		if(v[0]>1)
		    flag=0;
		for(auto it=m1.begin();it!=m1.end();it++)	
		{
			if(it->second>x)
			{
				f=1;
				break;
			}
			x=it->second;
		}
		x=-1;
		for(auto it=m2.begin();it!=m2.end();it++)	
		{
			if(it->second<x)
			{
				g=1;
				break;
			}
			x=it->second;
		}
		if(f==1||g==1||flag==0)
    		cout<<"NO"<<endl;
    	else
    	    cout<<"YES"<<endl;
	}
    return 0;
}
