You are given three strings A, B and C. Check whether they form a word chain.

More formally, determine whether both of the following are true:

* The last character in A and the initial character in B are the same.
* The last character in B and the initial character in C are the same.



If both are true, print `YES`. Otherwise, print `NO`.

Constraints

* A, B and C are all composed of lowercase English letters (`a` - `z`).
* 1 ≤ |A|, |B|, |C| ≤ 10, where |A|, |B| and |C| are the lengths of A, B and C, respectively.

Input

Input is given from Standard Input in the following format:


A B C


Output

Print `YES` or `NO`.

Examples

Input

rng gorilla apple


Output

YES


Input

yakiniku unagi sushi


Output

NO


Input

a a a


Output

YES


Input

aaaaaaaaab aaaaaaaaaa aaaaaaaaab


Output

NO
#include <bits/stdc++.h>
using namespace std;
vector<int> v;
int main() {
  long long int sum = 0;
  int A, B, C;
  scanf("%d %d %d", &A, &B, &C);
  sum = A % B;
  for (; true;) {
    if (sum == C) {
      printf("YES\n");
      return 0;
    } else if (find(v.begin(), v.end(), sum) != v.end() && *v.end() != sum) {
      printf("NO\n");
      return 0;
    } else {
      v.push_back(sum);
    }
    sum += A;
    sum %= B;
  }
  return 0;
}
