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

z=[int(x) for x in input().split()]
lim=max(z)
ctr=10000000

minz=[]
minz_num=[]#no. of moves for every element in z
for i in range (1,max(z)+1):
    strt=i
    moves=0
    for j in range (0,len(z)):
        if (z[j]!= strt+j*k):
            moves+=1
    minz.append(moves)
    minz_num.append(strt)



ansf=min(minz)
a=minz_num[minz.index(ansf)]

ans=""
for i in range (0,len(z)):
    if (z[i] > a+ i*k):
        ans+="-"+" "+str(i+1)+" "+str(abs(z[i]-a-i*k))+"\n"
    if (z[i] < a+i*k):
        ans+="+"+" "+str(i+1)+" "+str(abs(z[i]-a-i*k))+"\n"

print (ansf)
print (ans)
        
    
