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.
a=int(input())
z=list(map(int,input().split()))
z=z[::-1]
l=0
r=0
count=0

while(l<=r and r<len(z)):
    
    if(l==r):
    
        if(r+z[l]+1<len(z)):
            count+=z[l]
            r+=z[l]+1
        else:
            count+=len(z)-r-1
            r=len(z)
        l+=1
    else:
        if(z[l]<r-l):
            l+=1
        else:
            if(r+(z[l]-(r-l-1))<len(z)):
                
                count+=z[l]-(r-l-1)
                r+=z[l]-(r-l-1)
            else:
                count+=len(z)-r
                r=len(z)
            l+=1
print(len(z)-count)
        
        
    
   
    
