The Hailstone path for an integer **N** is the sequence, of numbers generated by the Hailstone function begin at **N** and ending at **1.** The Hailstone path length is the number of integers that appear on the Hailstone path, which is** 1 plus the number of times the hailstone function is called to reach 1. **i.e. h(n) = 1.

Such sequences are called hailstone sequences because the values typically rise and fall, somewhat analogously to a hailstone inside a cloud.

Program

Write a program to compute the Hailstone path of given N.

### Input

- The number(N) for which the hailstone path is to be computed.

### Output

- The total number in the path.
- The largest number in the path.

### Example

For example, the Hailstone path for number 12 is 12, 6, 3, 10, 15, 16, 8, 4, 2, 1.

The total numbers in the hailstone path are: 10

The largest number in the hailstone path is: 16

### Algorithm

For a given N, iterate using the following rule:

if N is an even number, the next number in the path is N = N/2, else N = 3N + 1.

Stop iterating the above rule, after the sequence 4, 2, 1 occurs.

### Test cases

No | Input N (How many numbers) | Intermediate (Path) | Output (Total, Largest) |
---|---|---|---|

1 | 12 | 12, 6, 3, 10, 15, 16, 8, 4, 2, 1 | 10,16 |

2 | 3 | 3,10, 5, 16, 8, 4, 2, 1 | 8,16 |

3 | 7 | 7, 22, 11, 34, 17, 52, 26, 13, 40, 20, 10, 5, 16, 8, 4, 2, 1 | 17,52 |

### Instructions

- Accept the number (N) for which the Hailstone path has to be computed as input via the command line arguments.
- Write the logic to compute the Hailstone numbers on the path, determine the length of the path along with the largest number in the path.
- Display the result i.e. Total and Largest separated by a comma.