Write a program to tell
if a given sequence of integer numbers x_{1} … 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 x_{1} … 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 ≤ 10^{4}.

Output

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

Public test cases

**Input**

7 5 -3 2 0 -1 3 2 0 3 -1 -1 -2 6 2 2 4 3 3 6

**Output**

yes yes yes no

Information

- Author
- Salvador Roura
- Language
- English
- Translator
- Salvador Roura
- Original language
- Catalan
- Other languages
- Catalan
- Official solutions
- C++
- User solutions
- C++