Two Cakes

Description:

Input:

The first line of the input contains an integer number $$$n$$$ — the number of tiers in each cake ($$$1 \le n \le 10^5$$$).

The second line contains $$$2 \cdot n$$$ integers $$$a_1, a_2, \dots, a_{2n}$$$ ($$$1 \le a_i \le n$$$), where $$$a_i$$$ is equal to the size of the tier, which can be bought in the $$$i$$$-th house. Remember that in each house you can buy only one tier. It is guaranteed that every number from $$$1$$$ to $$$n$$$ occurs in $$$a$$$ exactly two times.

Output:

Print one number  — the minimum distance that the guys have to walk in total to buy both cakes. Guys can be near same house at the same time. They begin near the first (leftmost) house. Each of the guys should buy $$$n$$$ tiers in ascending order of their sizes.

Sample Input:

3
1 1 2 2 3 3

Sample Output:

9

Sample Input:

2
2 1 1 2

Sample Output:

5

Sample Input:

4
4 1 3 2 2 3 1 4

Sample Output:

17

Note:

In the first example, the possible optimal sequence of actions is:

• Sasha buys a tier of size $$$1$$$ near the $$$1$$$-st house ($$$a_1=1$$$);
• Dima goes to the house $$$2$$$;
• Dima buys a tier of size $$$1$$$ near the $$$2$$$-nd house ($$$a_2=1$$$);
• Sasha goes to the house $$$4$$$;
• Sasha buys a tier of size $$$2$$$ near the $$$4$$$-th house ($$$a_4=2$$$);
• Sasha goes to the house $$$5$$$;
• Sasha buys a tier of size $$$3$$$ near the $$$5$$$-th house ($$$a_5=3$$$);
• Dima goes to the house $$$3$$$;
• Dima buys a tier of size $$$2$$$ near the $$$3$$$-rd house ($$$a_3=2$$$);
• Dima goes to the house $$$6$$$;
• Dima buys a tier of size $$$3$$$ near the $$$6$$$-th house ($$$a_6=3$$$).

So, Sasha goes the distance $$$3+1=4$$$, and Dima goes the distance $$$1+1+3=5$$$. In total, they cover a distance of $$$4+5=9$$$. You can make sure that with any other sequence of actions they will walk no less distance.