Balanced sequences P49052

Write a program to tell if a given sequence of integer numbers $x_1 \dots x_n$ is balanced or not. Let $m = \lceil n/2 \rceil$. In this problem, we say that a sequence is balanced if $n \le 2$, or if the left-hand half $x_1 \dots x_m$ and the right-hand half $x_{m+1} \dots x_n$ 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 $0 \le n \le 10^4$.

Output

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