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>
#include<iostream>
using namespace std;
#define int long long 
#define fi first 
#define se second 
#define mp make_pair 
#define pb push_back 
typedef pair<int, int >ii;
typedef pair<int, ii> iii;
const int INF = 1e15;
const int MOD = 1e9 + 7;
const int N = 1e5 + 5;
int i;
char st;
string s;
void solve() {
    cin >> s;
    set<char> st;
    for (char c : s) {
        st.insert(c);
    }
    bool flag = 0;
    for (char i = 'z'; i >= 'a'; i--) {
        if (flag) {
            if (s.size() == 0) {
                cout << "NO" << '\n';
                return;
            }
            if (s.front() != i && s.back() != i) {
                cout << "NO" << '\n';
                return;
            }
            else {
                if (s.front() == i) {
                    s.erase(0, 1);
                }
                else s.pop_back();
            }
        }
        else {
            if (st.count(i)) {
                flag = true;
                if (s.front() != i && s.back() != i) {
                    cout << "NO" << '\n';
                    return;
                }
                if (s.front() == i) {
                    s.erase(0, 1);
                }
                else s.pop_back();
            }
        }
    }
    if (s.size()) {
        cout << "NO" << '\n';
        return;
    }
    cout << "YES" << '\n';
}

int32_t main() {

    ios_base::sync_with_stdio(false);
    cin.tie(NULL);
 //   freopen("input.txt", "r", stdin);
 //   freopen("output.txt", "w", stdout);
    int t;
    cin >> t;
    while (t--) {
        solve();
    }
}