C. Binary String
time limit per test
1 second
memory limit per test
1024 megabytes
input
standard input
output
standard output

Given a binary string $$$S = S_1 S_2 \dots S_n$$$ of length $$$n$$$, you need to insert a bitwise operator between every two adjacent digits $$$S_i$$$ and $$$S_{i+1}$$$ (there are $$$n-1$$$ such positions), so that the final value of the resulting expression is $$$0$$$.

There are three operators to choose from, with the following rules:

  • Bitwise AND (&): for the expression $$$a$$$ & $$$b$$$, its value is $$$1$$$ if and only if $$$a=b=1$$$; otherwise, it is $$$0$$$.
  • Bitwise XOR (^): for the expression $$$a$$$ ^ $$$b$$$, its value is $$$1$$$ if and only if $$$a=1,b=0$$$ or $$$a=0,b=1$$$; otherwise, it is $$$0$$$.
  • Bitwise OR (|): for the expression $$$a$$$ | $$$b$$$, its value is $$$0$$$ if and only if $$$a=b=0$$$; otherwise, it is $$$1$$$.

Note that in this problem, the precedence of bitwise operators is the same as in C, according to the following rules:

  1. Bitwise AND (&) has the highest precedence.
  2. Bitwise XOR (^) has lower precedence than bitwise AND, but higher precedence than bitwise OR.
  3. Bitwise OR (|) has the lowest precedence.
  4. Operators with the same precedence are evaluated from left to right.

You need to construct a valid sequence of operators such that the final value of the whole expression is $$$0$$$. If there are multiple valid solutions, output any of them. It can be proved that for every valid input, at least one valid construction always exists.

Input

The first line contains a positive integer $$$n$$$ ($$$2 \le n \le 10^5$$$), which denotes the length of the string.

The second line contains a string $$$S$$$ of length $$$n$$$ consisting only of 0 and 1.

Output

Output one line containing a string of length $$$n-1$$$, representing the operators inserted in order. If there are multiple valid solutions, output any of them.

Example
Input
3
000
Output
&&
Note

In the sample, the original string is 000. Two bitwise AND operators can be inserted in the middle to make the expression 0&0&0, whose result is 0. Therefore, output &&.