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

dead = [0] * n
alive = n - 2
i = n - 1
done = False
while i > 0 and not done:
    while i <= alive and not done:
        alive -= 1
        if alive < 0:
            done = True
            break
    while i - L[i] <= alive and not done:
        #print "%d kills %d" % (i, alive)
        dead[alive] = 1
        alive -= 1
        if alive < 0:
            done = True
            break
    i -= 1
print n - sum(dead)
