Buy Low, Sell High

• 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:

1. You buy a share on day $a$ and sell it on day $b$ where $a \le b$.
   
2. 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.