## Osman and His Array

View as PDF

Points: 1
Time limit: 1.0s
Memory limit: 256M

Problem types

Osman has an array $$a_1$$, $$a_2$$,...,$$a_n$$.

In one operation, Osman chooses two different indices in the array $$p$$ and $$q$$ and decrease the integers $$a_p$$ and $$a_q$$ by one.

Osman wonders whether it is possible to make all the elements in the array zero or not. Can you help Osman find out?

#### Input

The first line contains the number $$N$$, the size of the array.

The second line contains $$N$$ integers, $$a_1$$, $$a_2$$,...,$$a_n$$, the elements of the array.

• $$2 \leq N \leq 10^5$$
• $$1 \leq a_i \leq 10^9$$

#### Output

If it is possible to make all the elements 0, you should print "YES". If it is not, you should print "NO".

#### Examples

Input 1:

4
4 4 7 7

Output 1:

YES

Input 2:

6
1 2 3 4 5 6

Output 2:

NO

#### Explanations

• In the first input, it is possible to make all the elements 0, by choosing the first 2 elements in 4 steps and choosing the last 2 elements in 7 steps, decreasing them by 1 each time.
• It is impossible to make them 0 in the second input.