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Rules

1396. Maximum. Version 2

Time limit: 1.0 second
Memory limit: 64 MB
Consider the sequence of numbers ai, i = 0, 1, 2, …, which satisfies the following requirements:
  • a0 = 0
  • a1 = 1
  • a2i = ai
  • a2i+1 = ai + ai+1
for every i = 1, 2, 3, … .
Write a program which for a given value of n finds the largest number among the numbers a0, a1, …, an.

Input

You are given several test cases (not more than 10 000). Each test case is a line containing an integer n (1 ≤ n < 1018). The last line of input contains 0.

Output

For every n in the input write the corresponding maximum value found.

Sample

inputoutput
5
10
0
3
4

Notes

This problem is the same as 1079 “Maximum” but with bigger limitations.
Problem Author: Prepared by Vladimir Yakovlev