Problem:
Score : 200 points

Problem Statement

Snuke is having a barbeque party.

At the party, he will make N servings of Skewer Meal.

Example of a serving of Skewer Meal

He has a stock of 2N skewers, all of which will be used in Skewer Meal. The length of the i-th skewer is L_i.
Also, he has an infinite supply of ingredients.

To make a serving of Skewer Meal, he picks 2 skewers and threads ingredients onto those skewers.
Let the length of the shorter skewer be x, then the serving can hold the maximum of x ingredients.

What is the maximum total number of ingredients that his N servings of Skewer Meal can hold, if he uses the skewers optimally?

Constraints

1≦N≦100

1≦L_i≦100

For each i, L_i is an integer.

Input

The input is given from Standard Input in the following format:

N
L_1 L_2 ... L_{2N}

Output

Print the maximum total number of ingredients that Snuke's N servings of Skewer Meal can hold.

Sample Input 1

2
1 3 1 2

Sample Output 1

3

If he makes a serving using the first and third skewers, and another using the second and fourth skewers, each serving will hold 1 and 2 ingredients, for the total of 3.

Sample Input 2

5
100 1 2 3 14 15 58 58 58 29

Sample Output 2

135

Solution in C (Clang 3.8.0) (judge verdict: Time Limit Exceeded)

#include<stdio.h>

int main(void) {
	int i, k ,l;
	int kei;
	int niku;
	long long int touri;
	long long int la;
	long long int hon;
	long long int ans = 0;
	int sozai[200][2] = {};
	scanf("%d",&hon);

	for(int i = 0; i < hon; i++) {
		scanf("%d",&sozai[i][0]);
		scanf("%d",&sozai[i][1]);
	}
	for(i = 0; i < hon; i++) {
		for(k = i+1; k < hon; k++) {
			touri = 1;
			kei = sozai[i][0] + sozai[i][1] + sozai[k][0] + sozai[k][1];
			niku = sozai[i][0] + sozai[k][0];
			for(l = kei; l > 1; l--) {
				if(l <= niku || l  <= kei - niku) {
					break;
				}
				touri *= l;
			}
			la = niku > (kei - niku) ? (kei - niku) : niku;
			for(l = la ; l > 1; l--) {
				touri /= l;
			}
			ans += touri;
			if(ans > 1000000007) ans %= 1000000007;
		}
	}
	printf("%d\n",ans);
	return 0;
}