Frog 1

Source: AtCoder

Version: Phuoc Hung OJ Extended

Problem Statement

There are $N$ stones with heights $h_i$. A frog starts at stone 1 and may jump to stone $i+1$ or $i+2$. A jump from $i$ to $j$ costs $|h_i-h_j|$. Find the minimum total cost to reach stone $N$.

Input

Line 1 contains $N$. Line 2 contains $N$ integers $h_1,h_2,\ldots,h_N$.

Output

Print the minimum total cost.

Subtasks

• Subtask 1 — 20 points: 2 <= N <= 20.
• Subtask 2 — 30 points: 2 <= N <= 2000.
• Subtask 3 — 50 points: 2 <= N <= 100000; 1 <= h_i <= 10000.

Examples

Input

4
10 30 40 20

Output

30

Explanation

An optimal route is $1\to2\to4$, with cost $|10-30|+|30-20|=30$.