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 = input()
l = map(int,raw_input().split(' '))
l2 = [0]*n
l1 = [0]*n
l.reverse()
for i in range(len(l)):
    if l[i]==0:
        continue
    if i+l[i]<n:
        l2[i+l[i]]+=1
    elif i!=n-1:
        l2[n-1]+=1
    if l[i]>=1 and i<n-1:
        l1[i+1]+=1
count = 0
curr = l2[n-1]-l1[n-1]
if curr == 0 and l1[n-1]==0:
    count+=1
for i in range(n-2,-1,-1):
    curr += l2[i]-l1[i]
    if curr==0 and l1[i]==0:
        count+=1
    
    
print count