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=list(map(int,input().split()))
k=n
p=-1
k1=0
for i in range(n-1,0,-1) :
    if p==-1 and l[i]>0 :
        k-=min(i,l[i])
        p=i
        k1=min(i,l[i])
    if   p-k1<=i  :
        1
    if l[i]==0 and i<p-k1 :
        p=-1
        k1=0
    b=min(i,l[i])
    if l[i]>0 and p-k1>=i :
        k-=b
        k1=b
        p=i
    if l[i]>0 and p-k1<i :
        if p-k1>i-b :
            k-=abs((p-k1)-(i-b))
            
            p=i
            k1=b
    
        
        
           
      
    
print(k)
    
