Polygon

题号：NC237309
时间限制：C/C++/Rust/Pascal 1秒，其他语言2秒
空间限制：C/C++/Rust/Pascal 256 M，其他语言512 M
64bit IO Format: %lld

题目描述

You have $n$ segments, which are numbered from $1$ to $n$ . The length of the $i$ -th segment is $a_i$ .
A simple polygon is a polygon that does not intersect itself and has no holes. Note that a simple polygon has at least $3$ edges and its area is not equal to $0$ .
Determine whether you can use all $n$ segments to form a simple polygon with $n$ edges. Note that each segment must be used exactly once.

输入描述:

The first line contains one single integer $n$ ( $3\le n \le 2\times 10^5$ ), denoting the number of segments.

The second line contains $n$ integers $a_i$ ( $1\le a_i\le 10^9$ ), denoting the length of the $i$ -th segment.

It is guaranteed that $\sum_{i=1}^na_i\le 2\times 10^9$ .

输出描述:

If you can use these  segments to form a simple polygon, output YES, otherwise NO.

示例1

输入

复制

3
3 4 5

输出

复制

YES

说明

In the first example, you can use them to construct a right-angled triangle

示例2

输入

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4
1 1 1 3

输出

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NO