892_B. Wrath
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.
```python
n=int(input())
l=[0]*n
r=[0]*n
len=list(map(int,input().split()))
for i in range(n):
    a=max(0,i-len[i])
    b=max(a,i)
    #print(' '.join(map(str,[i,a,b])))
    l[a]+=1
    r[b]+=1
ans=0
t=0
for i in range(n):
    t+=l[i]
    t-=r[i]
    #print('t='+str(t))
    if t==0:
        #print('i='+str(i))
        ans+=1
print(ans)
```