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 main():
    file=sys.stdin
    line=file.readline();
    values=line.split(' ')
    n,k=int(values[0]), int(values[1])
    h=[0]*n
    line=file.readline()
    values=line.split(' ')
    max_value=0
    for i in range(n):
        h[i]=int(values[i])
        if h[i]>max_value:
            max_value=h[i]
    max=0
    ans=[]
    for i in range(1,max_value+1):
        count=0
        tmp_ans=[]
        for j in range(n):
            if h[j]==i+j*k:
                count+=1
            elif h[j]<i+j*k:
                tmp_ans.append('+ '+str(j+1)+' '+str(i+j*k-h[j]))
            else:
                tmp_ans.append('- '+str(j+1)+' '+str(h[j]-(i+j*k)))
        if count>max:
            max=count
            ans=tmp_ans

    print n-max
    for s in ans:
        print s


main()