The Queen of England has n trees growing in a row in her garden. At that, the i-th (1 ≤ i ≤ n) tree from the left has height ai meters. Today the Queen decided to update the scenery of her garden. She wants the trees' heights to meet the condition: for all i (1 ≤ i < n), ai + 1 - ai = k, where k is the number the Queen chose.

Unfortunately, the royal gardener is not a machine and he cannot fulfill the desire of the Queen instantly! In one minute, the gardener can either decrease the height of a tree to any positive integer height or increase the height of a tree to any positive integer height. How should the royal gardener act to fulfill a whim of Her Majesty in the minimum number of minutes?

Input

The first line contains two space-separated integers: n, k (1 ≤ n, k ≤ 1000). The second line contains n space-separated integers a1, a2, ..., an (1 ≤ ai ≤ 1000) — the heights of the trees in the row. 

Output

In the first line print a single integer p — the minimum number of minutes the gardener needs. In the next p lines print the description of his actions. 

If the gardener needs to increase the height of the j-th (1 ≤ j ≤ n) tree from the left by x (x ≥ 1) meters, then print in the corresponding line "+ j x". If the gardener needs to decrease the height of the j-th (1 ≤ j ≤ n) tree from the left by x (x ≥ 1) meters, print on the corresponding line "- j x".

If there are multiple ways to make a row of trees beautiful in the minimum number of actions, you are allowed to print any of them.

Examples

Input

4 1
1 2 1 5


Output

2
+ 3 2
- 4 1


Input

4 1
1 2 3 4


Output

0
print(function(n, k) {
	var a = readline().split(' ').map(Number);
	var min = 1e6;
	var s = 0;
	for (var i = 1; i <= 1000; i++) {
		var x = 0;
		for (var j = 0; j < n; j++) {
			if (a[j] !== i + j * k) {
				x++;
			}
		}
		if (x < min) {
			min = x;
			s = i
		}
	}
	var ans = [];
	for (var i = 0; i < n; i++) {
		var x = s + i * k - a[i];
		if (x > 0) {
			ans.push('+ ' + (i + 1) + ' ' + x);
		} else if (x < 0) {
			ans.push('- ' + (i + 1) + ' ' + (-x));
		}
	}

	return ans.length == 0 ? ans.length : ans.length + '\n' + ans.join('\n')
}.apply(0, readline().split(' ').map(Number)));