B. Binary Substrings
time limit per test
2 seconds
memory limit per test
512 megabytes
input
standard input
output
standard output

Given an integer $$$n$$$, you need to find a string of length $$$n$$$ containing only $$$0$$$s and $$$1$$$s that maximize the number of different nonempty substrings.

Input

The only line contains a single integer $$$n$$$ ($$$1 \le n \le 2\times 10^5$$$), the length of the $$$01$$$-string.

Output

Output a single $$$01$$$-string of length $$$n$$$ that has the maximum number of different nonempty substrings among all the $$$01$$$-strings of length $$$n$$$. If there are multiple solutions, you may output any.

Examples
Input
2
Output
01
Input
5
Output
00110
Note

In the first sample case, there are $$$3$$$ different nonempty substrings "0", "1", and "01".

In the second sample case, there are $$$12$$$ different nonempty substrings "0", "1", "00", "01", "11", "10", "001", "011", "110", "0011", "0110", and "00110".