시간 제한 메모리 제한 제출 정답 맞은 사람 정답 비율
1 초 128 MB 7 6 5 83.333%

문제

A binary number is a number in base 2, where the individual digits, or bits, have weights in powers of two. For example, the decimal number 23 is written as 10111 in binary because:

(1 × 24) + (0 × 23) + (1 × 22) + (1 × 21) + (1 × 20) = (1 × 16) + (1 × 4) + (1 × 2) + (1 × 1) = 23.

A Gray code sequence consists of a sequence of binary values, in which each value differs from its immediate predecessor by only a single bit. The following example shows a standard Gray code sequence of 3-bit binary numbers.

Binary sequence 000 001 010 011 100 101 110 111
Standard Gray code sequence 000 001 011 010 110 111 101 100

A very simple algorithm is available to convert a binary number into its equicalent standard Gray code value. For example, to convert binary value 011, we start by copying the first bit:

0 1 1
v    
0    

To obtain the second bit, we add the first and second bits of the given binary number, to get the sum 0 + 1 = 1:

0 + 1 1
    v  
0   1  

To obtain the third bit, we add teh second and third bits of the given binary number, to get the sum 1 + 1 = 10 (in binary), but we discard the carry bit so we just take the rightmost bit 0 of the sum:

0 1 + 1
      v
0 1   0

Hence our answer is 010.

In general, except the first bit, the k-th bit of the standard Gray code is obtained by adding the (k-1)-th bit and the k-th bit of the given binary number and discarding the carry. The discard-carry addition operation can be described completely as:

  0    0    1    1
+ 0  + 1  + 0  + 1
---  ---  ---  ---
   0   1    1    0
---  ---  ---  ---

As another example, the 5-bit binary number 10101 is converted to its equivalent standard Gray code value 11111 by applying the above algorithm. The table below shows a few more examples.

Binary value Equivalent standard Gray code value
01110 01001
111111 100000
1001001 1101101
000111000 000100100

You are to write a program to convert an n-bit binary value into its equivalent n-bit standard Gray code value, where 1 ≤ n ≤ 20

입력

 

The input consists of two lines, each line containing one integer.

  1. The first line contains the integer n, the number of bits, where 1 ≤ n ≤ 20.
  2. The second line contains a bit-string of length n representing the n-bit binary number.

출력

The output contains a bit-string of length n representing the standard Gray code equivalent of the given n-bit binary number.

예제 입력 1

3
011

예제 출력 1

010