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.
alive = int(input())
claws = list(map(int, input().split()))
prev_beg, prev_end = (None, None)
for index, length in enumerate(reversed(claws)):
	beg = index + 1
	end = min(index + 1 + length, len(claws))
	if end - beg > 0:
		if prev_end and beg <= prev_end:
			prev_end = max(prev_end, end)
		else:
			if prev_end:
				alive -= prev_end - prev_beg
			prev_beg, prev_end = beg, end

if prev_end:
	alive -= prev_end - prev_beg
print(alive)