D - Zero Array

Go Free9192023-08-22 8:38

You are given an array a_1, a_2, \ldots, a_na1,a2,...,an.

In one operation you can choose two elements a_iai and a_jaj (i \ne ji=j) and decrease each of them by one.

You need to check whether it is possible to make all the elements equal to zero or not.

Input

The first line contains a single integer nn (2 \le n \le 10^52≤n≤105) --- the size of the array.

The second line contains nn integers a_1, a_2, \ldots, a_na1,a2,...,an (1 \le a_i \le 10^91≤ai≤109) --- the elements of the array.

Output

Print "YES" if it is possible to make all elements zero, otherwise print "NO".

Sample 1

Inputcopy	Outputcopy
`4 1 1 2 2`	`YES`

Sample 2

Inputcopy	Outputcopy
`6 1 2 3 4 5 6`	`NO`

Note

In the first example, you can make all elements equal to zero in 33 operations:

Decrease a_1a1 and a_2a2,
Decrease a_3a3 and a_4a4,
Decrease a_3a3 and a_4a4

In the second example, one can show that it is impossible to make all elements equal to zero.

复制代码

#include<iostream>
#include<algorithm>
using namespace std;
typedef long long ll;
ll n;
ll sum = 0;
int main()
{
	ll maxnum = 0;
	cin >> n;
	for (ll i = 0; i < n; i++)
	{
		ll num;
		cin >> num;
		sum += num;
		maxnum = max(maxnum, num);
	}
	//因为是成对成对的减少，所以总数首先是偶数。其次还要满足最大的数小于等于总数的一半，这样才能保证最大的数消去
	if (sum % 2 == 0&&maxnum <= sum / 2) cout << "YES" << endl;
	else cout << "NO" << endl;
}