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B. Wrath

time limit per test

2 secondsmemory limit per test

256 megabytesinput

standard inputoutput

standard outputHands 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.

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.

Codeforces (c) Copyright 2010-2023 Mike Mirzayanov

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