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
'''
Created on May 7, 2014

@author: Ved

Codeforces 402B
'''


def main():
    n,k = map(int, raw_input().split())
    a = map(int, raw_input().split())
    
    solve(n,k,a)
    
def solve(n,k,a):
    minchanges = n
    changes = []
    kchanges = []
    for start in xrange(1,1001):
        count = 0
        test = [start + k*i for i in xrange(n)]
        tchanges = []
        for j in xrange(n):
            tchanges.append(test[j]-a[j])
            if test[j] != a[j]:
                count += 1
        if count < minchanges:
            minchanges = count
            changes = test
            kchanges = tchanges
            
    print minchanges
    for i in xrange(len(kchanges)):
        if kchanges[i] < 0:
            print "-", i+1, abs(kchanges[i])
        elif kchanges[i] > 0:
            print "+", i+1, kchanges[i]
            
            
    


if __name__ == "__main__":
    main()