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())
A = list(map(int,input().split()))
C = []
for i in range(len(A)):
    C.append(i+1-A[i])

k = 1   # последний себя не убъет

v = len(C)-1     # индекс последнего элемента
for i in range(len(C)-1,0,-1):
    t = C[i]   # индекс текущего игрока, начиная с t-1 элемента может шлепнуть
    if i == len(C)-1:
        if t-1 < v:
            v = t-1
    else:
        if t-1 >= i and i < v:   # может только себя или других выше
            k += 1
            v = i
            continue
        if t-1 >= i and i >= v:   #
            continue
        if t-1 < v:
             #  начиная с v всех убил
            if i < v:
                k += 1
            v = t - 1
if v > 0:
    k += v
print(k)