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 read_input():
  n = int(input())
  arr = input()
  arr = arr.split(" ")
  for i in range(0, n):
    arr[i] = int(arr[i])
  
  return n, arr

def solve(n, arr):
  alive = []
  for i in range(0, n):
    alive.append(0)

  count = 0

  for i in range(n-1, -1,-1):
    if count > 0:
      alive[i]=1
      count-=1
      count = max(count, arr[i])

    if count == 0:
      count+= arr[i]

  result = 0

  for i in range(0, n):
    if alive[i] == 0:
      result+=1
  

  
  print(result)

  
if __name__ == "__main__":
    n, arr = read_input()
    solve(n, arr)

