Problem:
Score : 500 points

Problem Statement

There are N integers, A_1, A_2, ..., A_N, written on a blackboard.

We will repeat the following operation N-1 times so that we have only one integer on the blackboard.

Choose two integers x and y on the blackboard and erase these two integers. Then, write a new integer x-y.

Find the maximum possible value of the final integer on the blackboard and a sequence of operations that maximizes the final integer.

Constraints

2 \leq N \leq 10^5

-10^4 \leq A_i \leq 10^4

All values in input are integers.

Input

Input is given from Standard Input in the following format:

N
A_1 A_2 ... A_N

Output

Print the maximum possible value M of the final integer on the blackboard, and a sequence of operations x_i, y_i that maximizes the final integer, in the format below.

Here x_i and y_i represent the integers x and y chosen in the i-th operation, respectively.

If there are multiple sequences of operations that maximize the final integer, any of them will be accepted.

M
x_1 y_1
:
x_{N-1} y_{N-1}

Sample Input 1

3
1 -1 2

Sample Output 1

4
-1 1
2 -2

If we choose x = -1 and y = 1 in the first operation, the set of integers written on the blackboard becomes (-2, 2).

Then, if we choose x = 2 and y = -2 in the second operation, the set of integers written on the blackboard becomes (4).

In this case, we have 4 as the final integer. We cannot end with a greater integer, so the answer is 4.

Sample Input 2

3
1 1 1

Sample Output 2

1
1 1
1 0

Solution in C++14 (GCC 5.4.1) (judge verdict: Wrong Answer)

#include <iostream>
#include <algorithm>
const int maxn=1e6+100;
using namespace std;
long long a[maxn];
int main(){
	ios::sync_with_stdio(false);
	cin.tie(0);
	int n;
	cin >> n;
	for (int i=1;i<=n;i++) cin >> a[i];
	sort(a+1,a+1+n);
	int l=1,r=n,cnt=0;
	bool flag=n%2==1?1:0;
	for (int i=1;i<=n;i++)
		if (a[i]<0) cnt++;
long long ans;
//cout << cnt;
	if (cnt<=n/2){
		ans=0;
		for (int i=1;i<=n;i++)
			ans+=i<=n/2?-a[i]:a[i];
		cout << ans << endl;
	// }
		for (;l<r;){
		if (flag){
			flag = 0;
			cout << a[l] << ' ' << a[r]<<endl;
			a[l] = a[l]-a[r--];
		}else{
			flag = 1;
			cout << a[r] << ' ' << a[l]<<endl;
			a[r] = a[r] - a[l++];
		}
	}

	}else{
		ans=0;//puts("fuck");
		for (int i=1;i<=n;i++)
			ans+=i<=cnt?-a[i]:a[i];
		cout << ans << endl;
	// }
		flag=0;
		for (;l<r && l<n-cnt+1;){
		if (flag){
			flag = 0;
			cout << a[l] << ' ' << a[r]<<endl;
			a[l] = a[l]-a[r--];
		}else{
			flag = 1;
			cout << a[r] << ' ' << a[l]<<endl;
			a[r] = a[r] - a[l++];
	}
}
	int tot=flag?a[r]:a[l];
	for (int i=n-cnt+1;i<=cnt;i++){
		cout << tot <<' '<<a[i]<<endl;
		tot-=a[i];
		//cout << "fuck";
	}
}

	
	// 	ans=0;
	// 	for (int i=1;i<=n;i++)
	// 		ans+=i<=n/2?-a[i]:a[i];
	// 	cout << ans << endl;
	// // }
	// for (;l<r;){
	// 	if (flag){
	// 		flag = 0;
	// 		cout << a[l] << ' ' << a[r]<<endl;
	// 		a[l] = a[l]-a[r--];
	// 	}else{
	// 		flag = 1;
	// 		cout << a[r] << ' ' << a[l]<<endl;
	// 		a[r] = a[r] - a[l++];
	// 	}
	// }
}