Write a code in C.

The following iterative sequence is defined for the set of positive integers:

n → n/2 (n is even) n → 3n + 1 (n is odd)

Using the rule above and starting with 13, we generate the following sequence:

13 → 40 → 20 → 10 → 5 → 16 → 8 → 4 → 2 → 1

It can be seen that this sequence (starting at 13 and finishing at 1) contains 10 terms. Although it has not been proved yet (Collatz Problem), it is thought that all starting numbers finish at 1.

Given n, output which starting number, under n, produces the longest chain. (If there are multiple starting numbers that produces longest chain, output the largest possible starting number, under n).

NOTE: Once the chain starts the terms are allowed to go above the value of n.

Sample input:

1000

Sample output:

871