A. Make it Increasing
time limit per test
2 seconds
memory limit per test
256 megabytes
input
standard input
output
standard output

You are given an array $$$a$$$ consisting of $$$n$$$ positive integers, and an array $$$b$$$, with length $$$n$$$. Initially $$$b_i=0$$$ for each $$$1 \leq i \leq n$$$.

In one move you can choose an integer $$$i$$$ ($$$1 \leq i \leq n$$$), and add $$$a_i$$$ to $$$b_i$$$ or subtract $$$a_i$$$ from $$$b_i$$$. What is the minimum number of moves needed to make $$$b$$$ increasing (that is, every element is strictly greater than every element before it)?

Input

The first line contains a single integer $$$n$$$ ($$$2 \leq n \leq 5000$$$).

The second line contains $$$n$$$ integers, $$$a_1$$$, $$$a_2$$$, ..., $$$a_n$$$ ($$$1 \leq a_i \leq 10^9$$$) — the elements of the array $$$a$$$.

Output

Print a single integer, the minimum number of moves to make $$$b$$$ increasing.

Examples
Input
5
1 2 3 4 5
Output
4
Input
7
1 2 1 2 1 2 1
Output
10
Input
8
1 8 2 7 3 6 4 5
Output
16
Note

Example $$$1$$$: you can subtract $$$a_1$$$ from $$$b_1$$$, and add $$$a_3$$$, $$$a_4$$$, and $$$a_5$$$ to $$$b_3$$$, $$$b_4$$$, and $$$b_5$$$ respectively. The final array will be [$$$-1$$$, $$$0$$$, $$$3$$$, $$$4$$$, $$$5$$$] after $$$4$$$ moves.

Example $$$2$$$: you can reach [$$$-3$$$, $$$-2$$$, $$$-1$$$, $$$0$$$, $$$1$$$, $$$2$$$, $$$3$$$] in $$$10$$$ moves.