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
class CodeforcesTask402BSolution:
    def __init__(self):
        self.result = ''
        self.n_k = []
        self.heights = []

    def read_input(self):
        self.n_k = [int(x) for x in input().split(" ")]
        self.heights = [int(x) for x in input().split(" ")]

    def process_task(self):
        w_k = 1001
        chosen = -1
        for base in range(1, 1001):
            costs = sum([0 if self.heights[x] == base + self.n_k[1] * x else 1 for x in range(self.n_k[0])])
            if costs < w_k:
                chosen = base
                w_k = costs
        operations = []
        for x in range(self.n_k[0]):
            if self.heights[x] != chosen + self.n_k[1] * x:
                diff = (chosen + self.n_k[1] * x) - self.heights[x]
                sign = "+" if diff > 0 else "-"
                operations.append("{0} {1} {2}".format(sign, x + 1, abs(diff)))
        self.result = "{0}\n{1}".format(len(operations), "\n".join(operations))

    def get_result(self):
        return self.result


if __name__ == "__main__":
    Solution = CodeforcesTask402BSolution()
    Solution.read_input()
    Solution.process_task()
    print(Solution.get_result())
