# Challenges

Problem Statement

Students of Cambridge University went for a Hack-a-thon in Massachusetts. They decided to stay there overnight. So they all went in a hotel named Hawthorne Hotel.
The hotel is represented here by a rectangular matrix of rooms. Matrix cell value contains the cost of that room. Some of the rooms in the hotel are available for free (cost=0). Upon further investigation by the President Nicole, he got to know that the rooms are for free because they are haunted. So, being responsible for the safety of all the team members, he decided not to book the rooms if it satisfies any of the below conditions:
1] Room is haunted
2] Room's below a haunted room in same column
These rooms are unsafe!
Help Nicole to calculate the total price of all the suitable safe rooms for the team.

Input

[2 Dimensional array]
The first line contains a positive integer N(number of rows) and M(number of columns) Each of the next N lines contains M space separated integers denoting a row of the matrix. Each element of the matrix represent the cost of that room.

Output

Single integer denoting the sum of the cost of all the safe rooms

Constraints

1 ≤ matrix.length ≤ 5
1 ≤ matrix[i].length ≤ 5
0 ≤ matrix[i][j] ≤ 10

Sample Input

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

Sample Output

7

Dcoded By: Rajat Gupta

Solved By: 301

Maximum Marks: 12