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
import sys

def compute_min(i, trees, k):
    ctr = 0
    acts = []
    for j in range(len(trees)):
        new_h = trees[i] + (j-i) * k
        if new_h <= 0:
            return -1, []
        else:
            if trees[j] != new_h:
                ctr += 1
                diff = trees[j] - new_h
                if diff > 0:
                    acts.append("- " + str(j+1) + " " + str(diff))
                else:
                    acts.append("+ " + str(j+1) + " " + str(-diff))

    return ctr, acts



if __name__ == "__main__":
    line = sys.stdin.readline()
    items = line.split()
    n = int(items[0])
    k = int(items[1])
    line = sys.stdin.readline()
    trees = line.split()
    trees = [int(e) for e in trees]
    
    min_step = 1000000
    opti_acts = []
    # fix ith height
    for i in range(n):
        step, actions = compute_min(i, trees, k)
        if step >= 0 and step < min_step:
            min_step = step
            opti_acts = actions

    print min_step
    
    for act in opti_acts:
        print act
    
