Balanced sequences P49052

Write a program to tell if a given sequence of integer numbers x₁ … x_n is balanced or not. Let m = ⌈ n/2 ⌉. In this problem, we say that a sequence is balanced if n ≤ 2, or if the left-hand half x₁ … x_m and the right-hand half x_m+1 … x_n have the same sum, and both are balanced.

For instance, the sequence 5 -3 2 0 -1 3 2 is balanced, because the sum of 5 -3 2 0 and the sum of -1 3 2 are 4, and it is easy to see that both sequences are balanced.

Input

Input consists of several cases. Every one begins with n, followed ny n integer numbers. You can assume 0 ≤ n ≤ 10⁴.

Output

For every case, print “yes” or “no” as required.