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
import sys

line = sys.stdin.readline()
a=line.split()
n = int(a[0])
k = int(a[1])

line = sys.stdin.readline()
a = line.split()
heights = []
i = 0
maxH = 1
while(i<n):
    num = int(a[i])
    heights.append(num)
    if(maxH < num):
        maxH = num
    i += 1

h = 1
minMoves= n
moves = []
r= range(0,n)
while (h <= maxH):
    newH = [h + k*i for i in r]
    diff = [newH[i] - heights[i] for i in r]
    nonZero = [e for e in diff if e != 0]
    if(len(nonZero) <= minMoves):
        minMoves = len(nonZero)
        moves = diff    
    h+=1

print minMoves
for i in r:
    if moves[i]!=0:
        if moves[i] > 0:
            print "+ " + str(i+1) + " " + str(moves[i])
        else:
            print "- " + str(i+1) + " " + str(abs(moves[i]))
