Hands that shed innocent blood!

There are $*n*$ guilty people in a line, the $*i*$-th of them holds a claw with length $*L*_{*i*}$. 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 $*j* ≥ *i* - *L*_{*i*}$.

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 $*n*$ ($1 ≤ *n* ≤ 10^{6}$) — the number of guilty people.

Second line contains $*n*$ space-separated integers $*L*_{1}, *L*_{2}, ..., *L*_{*n*}$ ($0 ≤ *L*_{*i*} ≤ 10^{9}$), where $*L*_{*i*}$ is the length of the $*i*$-th person's claw.

Output

Print one integer — the total number of alive people after the bell rings.

Note

In first sample the last person kills everyone in front of him.