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
def check_bounds(start):
    return heights[start]-start*k >= 1

n,k = map(int,input().split())
heights = list(map(int,input().split()))
seq_start = -1
lon_seq = [0]*n
max_len = 0
cur_seq= [0]*n
cur_len=0
for i,a in enumerate(heights):
    cur_seq=[0]*n
    cur_len=0
    if check_bounds(i):
        for j,b in enumerate(heights):
            if b == a+(j-i)*k:
                cur_seq[j]=1
                cur_len+=1
        if cur_len>max_len:
            lon_seq=cur_seq
            max_len=cur_len
            seq_start=i
print(n-max_len)
for i,a in enumerate(heights):
    if lon_seq[i] != 1:
       diff=a-(heights[seq_start]+(i-seq_start)*k)
       if diff>0:
           print('{0} {1} {2}'.format('-',i+1,abs(diff)))
       else:
           print('{0} {1} {2}'.format('+',i+1,abs(diff)))

