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 raw_input().split()]
#import timeit

def first(n, L):
    alive = [1] * n
    mi = 0
    for i in range(n):
        if i % 1000 == 0: mi = alive.index(1)
        m = max(i-L[i], mi)
        alive[m:i] = [0] * (i-m)
    return sum(alive)

def second(n, L):
    alive = 0
    dead = 0
    L.reverse()
    for kill in L:
        if dead <= 0:
            alive += 1
        dead = max(dead - 1, kill)
    return alive

#n = 10
#L = [1, 1, 3, 0, 0, 0, 2, 1, 0, 3]
#print(first(n, L))
print(second(n, L))

#print timeit.timeit('first(10, L)', setup="from __main__ import first, n, L")
#print timeit.timeit('second(10, L)', setup="from __main__ import second, n, L")