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
In = lambda:map(int,raw_input().split())

n,k = In()
a = In()

res = 0
best = 1

cnt = 0;
for i in a:
    first_h = i - cnt * k
    
    if (first_h <= 0): continue
    res1 = 0
    
    cnt1 = 0
    for j in a:
        if (j == first_h + cnt1 * k): res1 += 1
        cnt1 += 1
        
    if (res1 > res): 
        res = res1
        best = first_h
        
    cnt += 1

print n-res

if(n-res > 0):
    cnt = 0
    for i in a:
        if (i - best - cnt * k > 0):
            print "-", cnt+1, abs(i - best  - cnt * k)
        if (i - best - cnt * k < 0):
            print "+", cnt+1, abs(i - best  - cnt * k)   
        cnt += 1