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.
n = int(input())
l = [int(i) for i in input().split(' ')]

cur_range = []
s = 0

for i in range(n-1,0,-1):
    if l[i] != 0:
        st = i - l[i]
        if st < 0: st = 0
        r = (st, i-1)
        if cur_range == []:
            cur_range.append(r)
            s += r[1] - r[0] + 1
        else:
            cur = cur_range[-1]
            if r[1] < cur[0]:
                cur_range.append(r)
                s += r[1] - r[0] + 1
            else:
                if r[0] >= cur[0]:
                    continue
                cur_range[-1] = (r[0], cur[1])
                s += cur[1] - r[0] - (cur[1] - cur[0])

print(n - s)