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
def LI(): return [int(x) for x in input().split(" ")]
def LS(): return [str(x) for x in input().split(" ")]
def ItoS(L): return [str(x) for x in L]
def StoI(L): return [int(c) for c in L]


def solve():
    n, t = LI()
    T = LI()
    sentou = [0] * (T[-1] + t + 1)
    
    i = 0
    while i < len(T):
        sentou[T[i]] += 1
        sentou[T[i] + t] -= 1
        i += 1

    j = 1
    while j < len(sentou):
        sentou[j] += sentou[j - 1]
        j += 1

    print(n * t - (sum(sentou) - (sentou.count(1) + len(sentou) - sentou.count(1) - sentou.count(0))))

solve()