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You are given an even integer $n$. Construct a binary number $a = \overline{a\_1 a\_2 \ldots a\_n}$ consisting of $n$ binary digits such that it is divisible by $n$, and all numbers $\overline{a\_1 a\_2 \ldots a\_i}$ (the prefixes of $a$ in binary notation) for $i = 1, 2, \ldots, n$ have different remainders modulo $n$.

The only line of input contains an integer $n$ ($2 \le n \le 1000$, $n$ is even).

Print the desired number $\overline{a\_1 a\_2 \ldots a\_n}$ as a string of $n$ binary digits. Leading zeroes are disallowed. If there are several possible answers, print any one of them. It is guaranteed that at least one answer exists under these constraints.