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 JavaScript (node.js v5.12) (judge verdict: Wrong Answer)

// inputに入力データ全体が入る
function Main(input) {
	input = input.split("\n");
	const N = parseInt(input[0]);
	const nums = input[1].split(" ").map(x => parseInt(x)).sort((a,b) => a > b ? -1 : a == b ? 0 : 1);
	var max = 0;
	for(i=0; i < N; i++){
		if(i % 2 == 0){
			max = max + nums[Math.floor(i/2)];
		}else{
			max = max - nums[N-Math.floor(i/2 + 1)];
		}
	}
	console.log(max);
	if(N % 2 == 0){
		var now = nums[N-1];
		for(i=1; i < N; i++){
			if(i % 2 == 0){
				console.log(nums[Math.floor(i/2)] + " " + now);
				now = nums[Math.floor(i/2)]-now;
			}else{
				console.log(nums[N-Math.floor(i/2 + 1)] + " " + now);
				now = nums[N-Math.floor(i/2 + 1)]-now;
			}
		}
	}else{
		var now = nums[0];
		for(i=1; i < N; i++){
			if(i % 2 == 0){
				console.log(nums[Math.floor(i/2)] + " " + now);
				now = nums[Math.floor(i/2)]-now;
			}else{
				console.log(nums[N-Math.floor(i/2 + 1)] + " " + now);
				now = nums[N-Math.floor(i/2 + 1)]-now;
			}
		}
	}
}
//*この行以降は編集しないでください（標準入出力から一度に読み込み、Mainを呼び出します）
Main(require("fs").readFileSync("/dev/stdin", "utf8"));