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(raw_input())
length = map(int, raw_input().split())

kill_count = 0
last_alive = n - 2

for current_person in xrange(n - 1, -1, -1):
    kill_farthest = max(current_person - length[current_person], 0)
    last_alive = min(last_alive, current_person - 1)
    if kill_farthest <= last_alive:
        kill_count += last_alive - kill_farthest + 1
        last_alive = kill_farthest - 1
        if last_alive == -1:
            break

print n - kill_count
