testcases:
  - name: "testcase 1"
    inputs:
    - 1 : 18
    output: 
    - 1 : [0, 1, 1, 2, 1, 2, 2, 3, 1, 2, 2, 3, 2, 3, 3, 4, 1, 2, 2]

  - name: "testcase 2"
    inputs:
    - 1: 23
    output:
    - 1 : [0, 1, 1, 2, 1, 2, 2, 3, 1, 2, 2, 3, 2, 3, 3, 4, 1, 2, 2, 3, 2, 3, 3, 4]

  - name: "testcase 3"
    inputs:
    - 1 : 33
    output: 
    - 1 : [0, 1, 1, 2, 1, 2, 2, 3, 1, 2, 2, 3, 2, 3, 3, 4, 1, 2, 2, 3, 2, 3, 3, 4, 2, 3, 3, 4, 3, 4, 4, 5, 1, 2]

  - name: "testcase 4"
    inputs:
    - 1: 67
    output:
    - 1 : [0, 1, 1, 2, 1, 2, 2, 3, 1, 2, 2, 3, 2, 3, 3, 4, 1, 2, 2, 3, 2, 3, 3, 4, 2, 3, 3, 4, 3, 4, 4, 5, 1, 2, 2, 3, 2, 3, 3, 4, 2, 3, 3, 4, 3, 4, 4, 5, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 1, 2, 2, 3]

  - name: "testcase 5"
    inputs:
    - 1: 14
    output:
    - 1 : [0, 1, 1, 2, 1, 2, 2, 3, 1, 2, 2, 3, 2, 3, 3]