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 math
def main():
    n,k = [int(i) for i in input().split()]
    l = [int(i) for i in input().split()]
    l2 = [l[i] - i*k for i in range(len(l))]
    d = dict()
    m = 0
    mn = 0
    for i in l2:
        if i > 0:
            try:
                d[i] += 1
            except:
                d[i] = 1
            if d[i] > m:
                m = d[i]
                mn = i
    count = 0
    ans = []
    for i in range(len(l2)):
        if l2[i] != mn:
            ans += [('+' if l2[i] < mn else '-') + ' ' + str(i+1) + ' ' + str(abs(l2[i] - mn))]
            count += 1
    print(count)
    for i in ans:
        print(i)

if __name__ == '__main__': main()
