**Time limit:**1.00 s**Memory limit:**512 MB

You know the stock price of a company during the next n days.

You will buy and sell a single share *exactly two times* during the period. More precisely, you will do as follows:

- You buy a share on day a and sell it on day b where a \le b.
- You buy a share on day c and sell it on day d where b \le c \le d.

How much money will you earn if you act optimally?

# Input

The first input line has an integer n: the number of days.

The second line has n integers p_1,p_2,\dots,p_n: the stock prices.

# Output

Print one integer: the maximum profit.

# Constraints

- 1 \le n \le 5 \cdot 10^5
- 1 \le p_i \le 10^9

# Example 1

Input:

8 4 2 3 5 1 4 2 7

Output:

9

Explanation: First you buy a share on day 2 and sell it on day 4. Then you buy a share on day 5 and sell it on day 8.

# Example 2

Input:

2 1 2

Output:

1

Explanation: First you buy a share on day 1 and sell it on day 2. Then you buy a share on day 2 and sell it on day 2.