Problem:
Score : 1600 points

Problem Statement

There is a rectangle in the xy-plane, with its lower left corner at (0, 0) and its upper right corner at (W, H). Each of its sides is parallel to the x-axis or y-axis. Initially, the whole region within the rectangle is painted white.

Snuke plotted N points into the rectangle. The coordinate of the i-th (1 ≦ i ≦ N) point was (x_i, y_i).

Then, for each 1 ≦ i ≦ N, he will paint one of the following four regions black:

the region satisfying x < x_i within the rectangle

the region satisfying x > x_i within the rectangle

the region satisfying y < y_i within the rectangle

the region satisfying y > y_i within the rectangle

Find the longest possible perimeter of the white region of a rectangular shape within the rectangle after he finishes painting.

Constraints

1 ≦ W, H ≦ 10^8

1 ≦ N ≦ 3 \times 10^5

0 ≦ x_i ≦ W (1 ≦ i ≦ N)

0 ≦ y_i ≦ H (1 ≦ i ≦ N)

W, H (21:32, added), x_i and y_i are integers.

If i ≠ j, then x_i ≠ x_j and y_i ≠ y_j.

Input

The input is given from Standard Input in the following format:

W H N
x_1 y_1
x_2 y_2
:
x_N y_N

Output

Print the longest possible perimeter of the white region of a rectangular shape within the rectangle after Snuke finishes painting.

Sample Input 1

10 10 4
1 6
4 1
6 9
9 4

Sample Output 1

32

In this case, the maximum perimeter of 32 can be obtained by painting the rectangle as follows:

Sample Input 2

5 4 5
0 0
1 1
2 2
4 3
5 4

Sample Output 2

12

Sample Input 3

100 100 8
19 33
8 10
52 18
94 2
81 36
88 95
67 83
20 71

Sample Output 3

270

Sample Input 4

100000000 100000000 1
3 4

Sample Output 4

399999994

Solution in Ruby (2.3.3) (judge verdict: Wrong Answer)

W, H, N = gets.strip.split(/ /).collect{|n| n.to_i}

x_list = []
y_list = []
N.times{
	x, y = gets.strip.split(/ /).collect{|n| n.to_i}
	x_list << x
	y_list << y
}

u_list = N.times.collect{|i| [i, y_list[i]]}.sort_by{|i, l| -l}
d_list = N.times.collect{|i| [i, H - y_list[i]]}.sort_by{|i, l| -l}
l_list = N.times.collect{|i| [i, x_list[i]]}.sort_by{|i, l| -l}
r_list = N.times.collect{|i| [i, W - x_list[i]]}.sort_by{|i, l| -l}

used = {}
count = 0

def get_cand(list, used)
	while used[list[-1][0]]
		list.pop
	end
	list[-1]
end

u_offset = 0
d_offset = 0
l_offset = 0
r_offset = 0


N.times{
	u_index, u_pos = get_cand(u_list, used)
	d_index, d_pos = get_cand(d_list, used)
	l_index, l_pos = get_cand(l_list, used)
	r_index, r_pos = get_cand(r_list, used)
	
	u_length = u_pos - u_offset
	d_length = d_pos - d_offset
	l_length = l_pos - l_offset
	r_length = r_pos - r_offset
	
	length = [u_length, d_length, l_length, r_length].min
	if u_length == length
		u_list.pop
		u_offset = u_pos
		used[u_index] = true
	elsif d_length == length
		d_list.pop
		d_offset = d_pos
		used[d_index] = true
	elsif l_length == length
		l_list.pop
		l_offset = l_pos
		used[l_index] = true
	else
		r_list.pop
		r_offset = r_pos
		used[r_index] = true
	end
}

puts ((W - l_offset - r_offset) + (H - u_offset - d_offset)) * 2