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
#!/usr/bin/env python

import sys
import logging
import traceback

logging.basicConfig(level = logging.INFO)

n, k = map(int, raw_input().split())

checked = [0] * n

nums = map(int, raw_input().split())

m = n + 1
ms = -1

for i in range(n) : 
    if checked[i] == 1 : 
        continue
    s = nums[i] - (i*k)
    if s <= 0 : 
        continue
    target = [s + j*k for j in range(n)]
    diff = 0
    for j in range(n) : 
        if target[j] != nums[j] : 
            diff += 1
        else : 
            checked[j] = 1
    if diff < m : 
        m = diff
        ms = s

print m 

target = [ms + j*k for j in range(n)]

for i in range(n) : 
    if target[i] != nums[i] : 
        if nums[i] < target[i] : 
            print "+ %d %d" %(i+1, abs(nums[i] - target[i]))
        else : 
            print "- %d %d" %(i+1, abs(nums[i] - target[i]))
