Hands that shed innocent blood!

There are *n* guilty people in a line, the *i*-th of them holds a claw with length *L*<sub class="lower-index">*i*</sub>. 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* &lt; *i* and *j* ≥ *i* - *L*<sub class="lower-index">*i*</sub>.

You are given lengths of the claws. You need to find the total number of alive people after the bell rings.
The first line contains one integer *n* (1 ≤ *n* ≤ 10<sup class="upper-index">6</sup>) — the number of guilty people.

Second line contains *n* space-separated integers *L*<sub class="lower-index">1</sub>, *L*<sub class="lower-index">2</sub>, ..., *L*<sub class="lower-index">*n*</sub> (0 ≤ *L*<sub class="lower-index">*i*</sub> ≤ 10<sup class="upper-index">9</sup>), where *L*<sub class="lower-index">*i*</sub> is the length of the *i*-th person's claw.
In first sample the last person kills everyone in front of him.
4
0 1 0 10
1
2
0 0
2
10
1 1 3 0 0 0 2 1 0 3
3
10
0 0 2 0 0 3 3 2 2 0
2
1
0
1
5
0 0 0 1 0
4
6
3 1 1 0 3 3
1
8
0 0 0 1 0 0 1 2
5
1
1000000000
1
2
1 3
1
2
1000000000 1000000000
1
11
1 0 0 1 1 3 2 0 0 2 3
4
1
1
1
n = int(input())
l2 = input().split()
claws = []
for i in range(n):
    claws.append(int(l2[i]))

alive = set([i for i in range(n)])
last_alive = 0
for i in range(n):
    if i - min(claws[i],i) <= last_alive <= i-1:
        alive = alive - set(range(last_alive,i))
        last_alive = i
    else:
        alive = alive - set(range(i-min(claws[i],i),i))

print(len(alive))