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 main():
    n = lie()
    a = array()
    dp = [0] * n
    for i in range(1, n):
        dp[max(0, i - a[i])] += 1
        dp[i] -= 1
    ans = 0
    for i in range(1, n):
        dp[i] += dp[i - 1]
    for i in range(n):
        if dp[i] == 0:
            ans += 1
    print(ans)


def fun(m, n, s, k):
    return


def fun2(s):
    return


from sys import *
import inspect
import re
from math import *
import threading
from collections import *
from pprint import pprint as pp
mod = 998244353
MAX = 10**5


def lie():
    return int(input())


def liee():
    return map(int, input().split())


def array():
    return list(map(int, input().split()))


def deb(p):
    for line in inspect.getframeinfo(inspect.currentframe().f_back)[3]:
        m = re.search(r'\bdeb\s*\(\s*([A-Za-z_][A-Za-z0-9_]*)\s*\)', line)
        print('%s %d' % (m.group(1), p))


def vector(size, val=0):
    vec = [val for i in range(size)]
    return vec


def matrix(rowNum, colNum, val=0):
    mat = []
    for i in range(rowNum):
        collumn = [val for j in range(colNum)]
        mat.append(collumn)
    return mat


def dmain():
    setrecursionlimit(100000000)
    threading.stack_size(40960000)
    thread = threading.Thread(target=main)
    thread.start()


if __name__ == '__main__':
    # main()
    dmain()
