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
string=str(input())
astring=str(input())+' '

word=''
alist=[]
n=int(string[:string.index(' ')])
k=int(string[string.index(' ')+1:])

for char in astring:
    if char!=' ':
        word+=char
    else:
        alist.append(int(word))
        word=''

minchange=n
mina=1000

for a in range(1,1001):
    blist=[x*k+a for x in range(0,n)]
    change=0

    for i in range(0,n):
        if alist[i]!=blist[i]:
            change+=1

        if change>=minchange:
            break

    if change<minchange:
        minchange=change
        mina=a

blist=[x*k+mina for x in range(0,n)]
changelist=[]

for i in range(0,n):
        if alist[i]>blist[i]:
            changelist.append('- '+str(i+1)+' '+str(alist[i]-blist[i]))
        elif alist[i]<blist[i]:
            changelist.append('+ '+str(i+1)+' '+str(blist[i]-alist[i]))

print(minchange)

if minchange>0:
    for change in changelist:
        print(change)