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
a = input()
a = a.split()
a = list(map(int,a))
n = a[0]
k = a[1]
h = input()
h = h.split()
h = list(map(int,h))
c = []
def make(h,x):
    global k
    r = list(range(x))
    r.reverse()
    counter = 0
    #print(r)
    for i in r:
        if (h[i+1] - h[i] != k):
            h[i] = h[i+1] - k
            counter += 1
    #print(list(range(x+1,n)))
    for i in range(x+1,n):
        if (h[i] - h[i-1] != k):
            h[i] = h[i-1] + k
            counter += 1
    if (min(h) <= 0):
        counter = 1000000
    return counter
def myPrint(h,x):
    global k
    #print(h)
    r = list(range(x))
    r.reverse()
    #print(r)
    for i in r:
        if (h[i+1] - h[i] != k):
            if (h[i] < h[i+1] - k):
                print('+',i+1,h[i+1] - k - h[i])
            else:
                print('-',i+1,-(h[i+1] - k - h[i]))
            h[i] = h[i+1] - k
    #print(list(range(x+1,n)))
    for i in range(x+1,n):
        if (h[i] - h[i-1] != k):
            if (h[i] < h[i-1] + k):
                print('+',i+1,h[i-1] + k - h[i])
            else:
                print('-',i+1,-(h[i-1] + k - h[i]))
            h[i] = h[i-1] + k
    return
for i in range(n):
    c.append(make(h.copy(),i))
m = c.index(min(c))
print(c[m])
myPrint(h,m)
