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 <iostream>
using namespace std;
typedef unsigned long long ll;
#define rep(i,a,n) for(ll i = (a);i < (n);i++)
#define lp(i,a,n) for(ll i = (a);i <= (n);i++)
#define MAX 50000000000000ull

int main(){
  ll a,b,c;
  cin >> a >> b >> c;
  if(a == b && c != 0){
    cout << "NO" << endl;
    return 0;
  }else if(a == i){
    cout << "YES" << endl;
    return 0;
  }
  rep(i,1,MAX){
    if(a * i % b == c){
      cout << "YES" << endl;
      return 0;
    }
  }
  cout << "NO" << endl;
  return 0;
}
