One of DB and TN common interests is traveling. One day, they went to Grand Line and found One Piece !

The One Piece treasure has n gold coins (n is even). Both them like gold coins, but they evaluate them as different values. So they decided to divide those coins by following method :

DB and TN do n / 2 steps, at each step, DB choose 2 coins, TN takes the coin that she evaluates it greater, and DB take the rest coin.

Let’s help DB find how to take the maximum value at possible.

Input

First line : a single integer n (n is even) – the number of coins

Second line : n integers a₁, a₂, …, a_n. a_i is the value of i^th coin that TN evaluates.

Third line : n integers b₁, b₂, …, b_n. b_i is the value of i^th coin that DB evaluates.

Output

First line : an integer S – the maximum value DB can take.

Last n / 2 lines : i^th line contains two number x and y (1 ≤ x, y ≤ n), are the indexes of two
coins that DB choose on i^th step. Each coin must be chose exact one time.

If there are multiple ways, just print any of them.

Constraints

2 ≤ n ≤ 500 000

1 ≤ a_i ≤ 10⁹

1 ≤ b_i ≤ 10⁹

Note that a₁, a₂, …, a_n are n distinct integers.

Example

Input:
6
6 10 11 18 5 14
1 7 6 12 15 1

Output: 
28
5 1
2 6
3 4

Warning: large Input/Output data, be careful with certain languages