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 dist(A, B):
    res = 0
    for i in range(len(A)):
        if(A[i] != B[i]):
            res += 1
    return res

def generate_new(number):
    global n, k
    R = [0] * n
    for i in range(n):
        R[i] = number 
        number += k
    return R

n, k = list(map(int, input().split()))
A = list(map(int, input().split()))
N = 1009
res = [0] * n
res_dist = N
for i in range(1, N):
    B = generate_new(i)
    cur_dist = dist(A, B)
    if(cur_dist < res_dist):
        res = B
        res_dist = cur_dist
print(res_dist)
for i in range(len(A)):
    if(A[i] < res[i]):
        print('+', i + 1, res[i] - A[i])
    elif(A[i] > res[i]):
        print('-', i + 1, A[i] - res[i])