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Monday 8 August 2022

[Solution] Lost Array Codeforces Solution




F. Lost Array
time limit per test
1 second
memory limit per test
25

a (1-indexed) of length n that contains information about the world and life. After that, he decided to convert it into the matrix b (0-indexed) of size (n+1)×(n+1) which contains information about the world, life and beyond.

Spyofgame converted a into b with the following rules.

  • bi,0=0 if 0in;
  • b0,i=ai if 1in;
  • bi,j=bi,j1bi1,j if 1i,jn.

Here  denotes the bitwise XOR operation.

Today, archaeologists have discovered the famous matrix b. However, many elements of the matrix has been lost. They only know the values of bi,n for 1in (note that these are some elements of the last column, not the last row).

Solution Click Below:-  👉CLICK HERE👈

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 occupied

The archaeologists want to know what a possible array of a is. Can you help them reconstruct any array that could be a?

Input

The first line contains a single integer n (1n5105).

The second line contains n integers b1,n,b2,n,,bn,n (0bi,n<230).

Output

If some array a is consistent with the information, print a line containing n integers a1,a2,,an. If there are multiple solutions, output any.

If such an array does not exist, output 1 instead.

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