URI Online Judge | 3025

Harvester

By MicrosoftRS Serbia

Timelimit: 1

It is Bubble Cup finals season and farmer Johnny Bubbles must harvest his bubbles. The bubbles are in a rectangular bubblefield formed of N x M square parcels divided into N rows and M columns. The parcel in ith row and jth column yields A i,j bubbles.

Johnny Bubbles has available a very special self-driving bubble harvester that, once manually positioned at the beginning of a row or column, automatically harvests all the bubbles in that row or column. Once the harvester reaches the end of the row or column it stops and must be repositioned. The harvester can pass through any parcel any number of times, but it can collect bubbles from the parcel only once.

Johnny is very busy farmer, so he is available to manually position the harvester at most four times per day. Johnny is also impatient, so he wants to harvest as many bubbles as possible on the first day. Please help Johnny to calculate what is the maximum number of bubbles he can collect on the first day.

Input

The first line contains two integers N and M (1 ≤ N , MN * M ≤ 105) - the bubblefield size.

Each of the next N lines contains M integers. The jth element in the ith line is A i,j (0 ≤ A i,j ≤ 109 ) — the yield of the parcel located in the ith row and the jth column.

Output

Output contains one integer number - maximum number of the bubbles Johnny can harvest on the first day.

Input Samples Output Samples

2 2
1 2
3 4

10

5 5
0 9 2 7 0
9 0 3 0 5
0 8 0 3 1 
6 7 4 3 9
3 6 4 1 0

80