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
n, k = map(int, input().split())
a = list(map(int, input().split()))
max_p = n
max_i = -1
for i in range(n):
    p = 0
    if a[i] - k * i >= 1:
        for j in range(n):
            if j < i:
                if a[j] != a[i] - k * (i - j):
                    p += 1
            else:
                if a[j] != a[i] + k * (j - i):
                    p += 1
        if p < max_p:
            max_p = p
            max_i = i
print(max_p)
for i in range(n):
    if i < max_i:
        if a[i] < a[max_i] - k * (max_i - i):
            print('+', i + 1, a[max_i] - k * (max_i - i) - a[i])
        else:
            if a[i] > a[max_i] - k * (max_i - i):
                print('-', i + 1, a[i] - (a[max_i] - k * (max_i - i)))
    else:
        if i > max_i:
            if a[i] < a[max_i] + k * (i - max_i):
                print('+', i + 1, a[max_i] + k * (i - max_i) - a[i])
            else:
                if a[i] > a[max_i] + k * (i - max_i):
                    print('-', i + 1, a[i] - (a[max_i] + k * (i - max_i)))
