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
def main():
    n,k=map(int,raw_input().split())
    trees=map(int,raw_input().split())

    test_trees=[trees[0]]
    for i in xrange(1,n):
        test_trees.append(test_trees[i-1]+k)
    #print test_trees
    mid=[0]*n
    for i in xrange(n):
        mid[i]=test_trees[i]-trees[i]
    counter={}
    for each in mid:
        if counter.has_key(each):
            counter[each]+=1
        else:
            counter[each]=1
    #print counter
    mp=sorted(counter.items(),key=lambda x:x[1], reverse=True)
    maxk,maxv=mp[0]
    #print maxk,maxv
    if maxv==n:
        print 0
        return
    #if maxk==0: #cur k is okay. started from 1one.

    for maxk,maxv in mp:

        if test_trees[0]-maxk <=0:
            continue


        if maxk!=0:
            for i in xrange(n):
                mid[i]-=maxk
        test_trees=[0]*n
        for i in xrange(n):
            test_trees[i]=trees[i]+mid[i]

        #print test_trees[i]
        



        print n-maxv
        for i in xrange(n):
            if mid[i]>0:
                print "+ %d %d"%(i+1,mid[i])
            elif mid[i]<0:
                print "- %d %d"%(i+1,-1*mid[i])
        break
    












main()