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
n, k = map(int, input().split())
a = list(map(int, input().split()))
vis = [False] * n
answer = 0
for i in range(n):
    t = 0
    if not vis[i]:
        for j in range(i, n):
            if not vis[j]:
                temp = a[j] - ((j - i) * k)
                x = temp - a[i]
                if x == 0:
                    t += 1
                    vis[j] = True
                if temp <= 0:
                    vis[j] = True
    if t > answer:
        answer = t
        poi = i
        val = a[i]
print(n - answer)
if answer != n:
    for i in range(n):
        x = a[i] - val - ((i - poi) * k)
        if x == 0:
            continue
        elif x > 0:
            print('{} {} {}'.format('-', i + 1, x))
        elif x < 0:
            print('{} {} {}'.format('+', i + 1, -x))
		 	   		 	  			  		    					 	