testcases:
  - name: "testcase 1"
    inputs:
    - 1 : 2
    - 2 : 2
    - 3 : [[1,1],[1,2],[2,1],[2,2]]
    output: 
    - 1 : 1
  - name: "testcase 2"
    inputs:
    - 1: 2
    - 2: 2
    - 3 : [[1,1],[2,1],[1,2],[2,2]]
    output:
    - 1 : 2
  - name: "testcase 3"
    inputs:
    - 1: 5
    - 2: 5
    - 3 : [ [1, 1], [2, 1], [3, 1], [4, 1], [5, 1],
            [1, 2], [2, 2], [3, 2], [4, 2], [5, 2],
            [1, 3], [2, 3], [3, 3], [4, 3], [5, 3],
            [1, 4], [2, 4], [3, 4], [4, 4], [5, 4],
            [1, 5], [2, 5], [3, 5], [4, 5], [5, 5]]
    output:
    - 1 : 20
  - name: "testcase 4"
    inputs:
    - 1: 3
    - 2: 3
    - 3 : [[1,2],[2,1],[3,3],[2,2],[1,1],[1,3],[2,3],[3,2],[3,1]]
    output:
    - 1 : 3
  - name: "testcase 5"
    inputs:
    - 1 : 3
    - 2 : 4
    - 3 : [[2,4],[1,3],[3,3],[2,1],[2,3],[2,2],[1,4],[3,1],[1,1],[1,2],[3,2],[3,4]]
    output: 
    - 1 : 5