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 <bits/stdc++.h>
#define ll long long
#define xx first
#define yy second

using namespace std;

const int N = 100000 + 5;
int info[N], n;
int x[N], y[N], tot;

inline int Find (int l, int r, int f) {
	if (l == r) {
		return f * info[l];
	}
	if (f == 1) {
		int a = info[r], b = Find (l, r - 1, -1);
		++tot;
		x[tot] = a;
		y[tot] = b;
		return a - b;
	}
	else {
		int a = info[l], b = Find (l + 1, r, 1);
		++tot;
		x[tot] = a;
		y[tot] = b;
		return a - b;
	}
}

int main () {
	#ifdef wll
	freopen ("testdata.in", "r", stdin);
	#endif
	scanf ("%d", &n);
	for (int i = 1; i <= n; ++i) {
		scanf ("%d", &info[i]);
	}
	sort (info + 1, info + n + 1);
	printf ("%d\n", Find (1, n, 1));
	for (int i = 1; i <= tot; ++i) {
		printf ("%d %d\n", x[i], y[i]);
	}
	return 0;
}