Hands that shed innocent blood!

There are n guilty people in a line, the i-th of them holds a claw with length Li. The bell rings and every person kills some of people in front of him. All people kill others at the same time. Namely, the i-th person kills the j-th person if and only if j < i and j ≥ i - Li.

You are given lengths of the claws. You need to find the total number of alive people after the bell rings.

Input

The first line contains one integer n (1 ≤ n ≤ 106) — the number of guilty people.

Second line contains n space-separated integers L1, L2, ..., Ln (0 ≤ Li ≤ 109), where Li is the length of the i-th person's claw.

Output

Print one integer — the total number of alive people after the bell rings.

Examples

Input

4
0 1 0 10


Output

1


Input

2
0 0


Output

2


Input

10
1 1 3 0 0 0 2 1 0 3


Output

3

Note

In first sample the last person kills everyone in front of him.
class CodeforcesTask892BSolution:
    def __init__(self):
        self.result = ''
        self.n = 0
        self.claws = []

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

    def process_task(self):
        kill = False
        living = 0
        kill_range = self.n + 1
        for x in range(self.n, 0, -1):
            if x < kill_range:
                kill = False
            if not kill:
                living += 1
            if self.claws[x - 1]:
                kill = True
                kill_range = min(kill_range, x - self.claws[x - 1])
        self.result = str(living)

    def get_result(self):
        return self.result


if __name__ == "__main__":
    Solution = CodeforcesTask892BSolution()
    Solution.read_input()
    Solution.process_task()
    print(Solution.get_result())
