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.
'''
Culprits are standing in a line.
Some of them have a claw in their hands
we know length of every claw.
At a particular time all having claw kill infrom of them with their claw.
count number of survivor


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
'''

nos_of_culprits = int(input())
culprits = [int(i) for i in input().split()]
survivor = 0
least = nos_of_culprits
pos = nos_of_culprits
while pos > 0:
    pos -= 1
    if pos < least:
        survivor +=1
    least = min(pos - culprits[pos], least)

print(survivor)