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 int long long

int main() {
#ifdef PDTH
  freopen("input.txt", "r", stdin);
  freopen("output.txt", "w", stdout);
#endif //PDTH
  ios_base::sync_with_stdio(false);
  cin.tie(NULL); cout.tie(NULL);
  int T; cin >> T;
  while (T--) {
    string s; cin >> s;
    int n = s.size();
    int cur = -1;
    bool ok = true;
    vector<int> a(27, 0);
    for(int i = 0; i < n; ++i) {
      if (s[i] == 'a') cur = i;
    }
    if (cur == -1) { cout << "NO\n"; continue; }
    a[0] = 1;
    for(int i = cur-1; i >= 0; --i) {
      if (s[i] < s[i+1] || a[s[i]-'a']) ok = false;
      else {
        a[s[i]-'a'] = 1;
      }
    }
    for(int i = cur+1; i < n; ++i) {
      if (s[i] < s[i-1] || a[s[i]-'a']) ok = false;
      else {
        a[s[i]-'a'] = 1;
      }
    }
    for(int i = 1; i < 27; ++i) {
      if (a[i] && !a[i-1]) ok = false;
    }
    cout << (ok ? "YES\n" : "NO\n");
  }
}