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
from sys import stdin ,stdout
from os import path
rd = lambda:stdin.readline().strip()
wr = stdout.write
if(path.exists('input.txt')):
    stdin = open("input.txt","r")
import time ,math
#------------------------------------=
x,y =map(int,rd().split())
mylist = list(map(int,rd().split()))
mn = 100000
first = 0
k = 1
while k <= 1000:
	counter = None
	if mylist[0] == k :
		counter = 0
	else:
		counter =  1
	
	arr = [k]
	for i in range(1,len(mylist)):
		if k+(i*y) != mylist[i]:
			counter+=1
	if counter< mn :
		mn = counter
		first = k

	if mn == 0 :
		break
	k+=1

arr = [first]
for _ in range(len(mylist)-1):
	arr.append(arr[-1]+y)
if mn == 0  :
	print(0)
else:
	print(mn)
	for i in range(len(mylist)):
		res = arr[i]- mylist[i]
		if res != 0 :
			if res< 0 :
				print('-',i+1,abs(res))
			else:
				print('+',i+1,abs(res))
