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;

#define ALL(v) v.begin(),v.end()
#define endl "\n"
#define FAST ios_base::sync_with_stdio(false); cin.tie(NULL);
#define MOD 1000000007
#define MAX 200005

#define CS(i) cout<<"Case "<<i<<": "

typedef long long ll;


void syntex_error()
{
    ll n,i,j,k;
    string s;
    cin>>s;

    ll id=-1;
    n=s.size();
    bool vis[30]={0};

    for(i=0; i<n; i++)
    {
        vis[s[i]-'a']=1;
        if(s[i]=='a')
        {
            id=i;
            //break;
        }
    }
    for(i=0; i<n; i++)
    {
        if(!vis[i])
        {
            id=-1;
            break;
        }
    }
    if(id==-1)
    {
        cout<<"NO"<<endl;
        return;
    }

    bool ok=1;
    for(i=id+1; i<n; i++)
    {
        if(s[i]<=s[i-1])
        {
            ok=0;
            break;
        }
    }

    for(i=0; i<id; i++)
    {
        if(s[i]<=s[i+1])
        {
            ok=0;
            break;
        }
    }

    if(ok)
    {
        cout<<"YES"<<endl;
    }
    else
    {
        cout<<"NO"<<endl;
    }
}

int32_t main()
{
    FAST
    
    ll TC=1LL,cs=1LL;

    cin>>TC;

    while(TC--){
        //CS(cs++);
        syntex_error();
    }

    return 0;
}