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.
# -*- coding: utf-8 -*-
"""
Created on Fri Dec  8 21:59:10 2017

@author: ms
"""

def kill(line, claws, i, omae_wa_mou_shindieru, dead_lim):
    if dead_lim > i:
        dead_lim = i
    reach = i - claws[i]
    if (reach <= 0):
        line[0:dead_lim] = [False for x in range(dead_lim)]
        claws[0:dead_lim] = [0 for x in range(dead_lim)]
        dead_lim = 0
        return line, claws, omae_wa_mou_shindieru, dead_lim
    
    for j in range(reach, dead_lim):
        if (j - claws[j]) >= reach:
            line[j] = False
            claws[j] = 0
        else:
            omae_wa_mou_shindieru.append(j)
        dead_lim = reach
    
    return line, claws, omae_wa_mou_shindieru, dead_lim
            
def main():
    line = []
    omae_wa_mou_shindeiru = []
    n = int(input())
    for k in range(n):
        line.append(True)
    
    dead_lim = n-1
    claws = [int(x) for x in input().split()]
    
    for i in reversed(range(n)):
        line, claws, omae_wa_mou_shindeiru, dead_lim = kill(line, claws, i, 
                                                            omae_wa_mou_shindeiru, 
                                                            dead_lim)
        if dead_lim == 0:
            break
        
    for el in omae_wa_mou_shindeiru:
        line[el] = False
    
    print(sum(line))
    
main()