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
inp = raw_input().split()
n, k = int(inp[0]), int(inp[1])

from math import fabs

def number_affected(L, a, k):
    acc = 0
    if L[1] != a + k: acc += 1
    for x in range(2, len(L)):
        if L[x] != a + (x * k): acc += 1
    if L[0] != a: acc += 1
    return acc


def find_tree(L, k):
    first = 1
    if len(L) == 1:
        print 0
        return
    min = number_affected(L, 1, k)
    for i in range(2, 1001):
        val = number_affected(L, i, k)
        if val < min:
            min = val
            first = i
    
    expected = first
    
    print min
    for i in range(len(L)):
        if L[i] != expected:
            if L[i] > expected:
                print "-", i + 1, (L[i] - expected)
            elif L[i] < expected:
                print  "+", i + 1, (expected - L[i])
        expected += k


find_tree([int(x) for x in raw_input().split()], k)
    
