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
import math,sys
#from itertools import permutations, combinations;import heapq,random;
from collections import defaultdict,deque
import bisect as bi
def yes():print('YES')
def no():print('NO')
def I():return (int(sys.stdin.readline()))
def In():return(map(int,sys.stdin.readline().split()))
def Sn():return sys.stdin.readline().strip()
#sys.setrecursionlimit(1500)
def dict(a):
    d={} 
    for x in a:
        if d.get(x,-1)!=-1:
            d[x]+=1
        else:
            d[x]=1
    return d
def find_gt(a, x):
    'Find leftmost value greater than x'
    i = bi.bisect_left(a, x)
    if i != len(a):
        return i
    else:            
        return -1
        
def main():
    try:
        n,k=In()
        l=list(In())
        mn=P
        ans=[]
        for i in range(1,1001):
            a=[]
            temp=i
            for j in range(n):
                if temp>l[j]:
                    a.append(['+',j+1,(temp-l[j])])
                elif temp<l[j]:
                    a.append(['-',j+1,(l[j]-temp)])
                temp+=k
            if len(a)<mn:
                ans=a.copy()
                mn=len(ans)
        print(mn)
        for x in ans:
            print(*x)

    except:
        pass
        
M = 998244353
P = 1000000007
 
if __name__ == '__main__':
    # for _ in range(I()):main()
    for _ in range(1):main()
#        *******************    All The Best    *******************   #