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.
def list_output(s):    
    print(' '.join(map(str, s)))
    
def list_input():
    return list(map(int, input().split()))

n = int(input())
L = list_input()

s = [0 for i in range(n+1)]
for i in range(n):
    j = i-L[i] # j >= i-L[i] and j < i    
    j = max(0, j)
    if j < i:
        s[j] -= 1
        s[i] += 1
t = [0 for i in range(n+1)]
for i in range(n):
    t[i+1] = t[i]+s[i]
res = 0
for i in range(1, n+1):
    if t[i] == 0:
        res += 1
#print(t)
print(res)