Educational Codeforces Round 27 E. Fire in the City(二维离散化)

The capital of Berland looks like a rectangle of size n × m of the square blocks of same size.

Fire!

It is known that k + 1 blocks got caught on fire (k + 1 ≤ n·m). Those blocks are centers of ignition. Moreover positions ofk of these centers are known and one of these stays unknown. Allk + 1 positions are distinct.

The fire goes the following way: during the zero minute of fire only these k + 1 centers of ignition are burning. Every next minute the fire goes to all neighbouring blocks to the one which is burning. You can consider blocks to burn for so long that this time exceeds the time taken in the problem. The neighbouring blocks are those that touch the current block by a side or by a corner.

Berland Fire Deparment wants to estimate the minimal time it takes the fire to lighten up the whole city. Remember that the positions ofk blocks (centers of ignition) are known and (k + 1)-th can be positioned in any other block.

Help Berland Fire Department to estimate the minimal time it takes the fire to lighten up the whole city.

Input

The first line contains three integers n,m and k (1 ≤ n, m ≤ 10⁹,1 ≤ k ≤ 500).

Each of the next k lines contain two integersx_i andy_i (1 ≤ x_i ≤ n,1 ≤ y_i ≤ m) — coordinates of thei-th center of ignition. It is guaranteed that the locations of all centers of ignition are distinct.

Output

Print the minimal time it takes the fire to lighten up the whole city (in minutes).

Examples

Input

7 7 31 22 15 5

Output

3

Input

10 5 13 3

Output

2分析;500个点,直接二分燃烧时间,每次暴力floodfill一下前缀和,然后再暴力扫一遍整个图找到横向的最远未燃烧块的距离和纵向的取最大值,如果最大值小于当前二分出的时间则说明我们可以通过再加一个燃烧块把这片区域覆盖住,总复杂度log*(500*2)^2