Problem:
Score : 1500 points

Problem Statement

We have a grid with 3 rows and N columns.
The cell at the i-th row and j-th column is denoted (i, j).
Initially, each cell (i, j) contains the integer i+3j-3.

A grid with N=5 columns

Snuke can perform the following operation any number of times:

Choose a 3×3 subrectangle of the grid. The placement of integers within the subrectangle is now rotated by 180°.

An example sequence of operations (each chosen subrectangle is colored blue)

Snuke's objective is to manipulate the grid so that each cell (i, j) contains the integer a_{i,j}.
Determine whether it is achievable.

Constraints

5≤N≤10^5

1≤a_{i,j}≤3N

All a_{i,j} are distinct.

Input

The input is given from Standard Input in the following format:

N
a_{1,1} a_{1,2} ... a_{1,N}
a_{2,1} a_{2,2} ... a_{2,N}
a_{3,1} a_{3,2} ... a_{3,N}

Output

If Snuke's objective is achievable, print Yes. Otherwise, print No.

Sample Input 1

5
9 6 15 12 1
8 5 14 11 2
7 4 13 10 3

Sample Output 1

Yes

This case corresponds to the figure in the problem statement.

Sample Input 2

5
1 2 3 4 5
6 7 8 9 10
11 12 13 14 15

Sample Output 2

No

Sample Input 3

5
1 4 7 10 13
2 5 8 11 14
3 6 9 12 15

Sample Output 3

Yes

The objective is already achieved with the initial placement of the integers.

Sample Input 4

6
15 10 3 4 9 16
14 11 2 5 8 17
13 12 1 6 7 18

Sample Output 4

Yes

Sample Input 5

7
21 12 1 16 13 6 7
20 11 2 17 14 5 8
19 10 3 18 15 4 9

Sample Output 5

No

Solution in Java8 (OpenJDK 1.8.0) (judge verdict: Wrong Answer)

import java.io.ByteArrayInputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.Arrays;
import java.util.InputMismatchException;

public class Main {
	static InputStream is;
	static PrintWriter out;
	static String INPUT = "";
	
	static void solve()
	{
		int n = ni();
		int[][] a = new int[3][];
		for(int i = 0;i < 3;i++){
			a[i] = na(n);
		}
		boolean[] spin = new boolean[n];
		int[] vs = new int[n];
		for(int i = 0;i < n;i++){
			if(
					a[0][i] % 3 == 1 && 
					a[1][i] == a[0][i] + 1 && 
					a[2][i] == a[1][i] + 1){
				spin[i] = false;
				int v = a[2][i] / 3;
				if(v % 2 == i % 2){
					out.println("No");
					return;
				}
				vs[i] = v;
			}else if(
					a[2][i] % 3 == 1 && 
					a[1][i] == a[2][i] + 1 && 
					a[0][i] == a[1][i] + 1){
				spin[i] = true;
				int v = a[0][i] / 3;
				if(v % 2 == i % 2){
					out.println("No");
					return;
				}
				vs[i] = v;
			}else{
				out.println("No");
				return;
			}
		}
		
		boolean[] base = new boolean[n];
		for(int i = 0;i < n;i++){
			if(((vs[i]-1)-i)/2%2 == 0){
				base[i] = false;
			}else{
				base[i] = true;
			}
		}
		{
			int[] ft = new int[n+3];
			for(int i = n-1;i >= 0;i--){
				if(i % 2 == 0){
					addFenwick(ft, vs[i], 1);
				}else{
					if(sumFenwick(ft, i)%2 == 1){
						base[i] = !base[i];
					}
				}
			}
		}
		{
			int[] ft = new int[n+3];
			for(int i = n-1;i >= 1;i--){
				if(i % 2 == 1){
					addFenwick(ft, vs[i], 1);
				}else{
					if(sumFenwick(ft, i)%2 == 1){
						base[i] = !base[i];
					}
				}
			}
		}
		
		for(int i = 0;i+2 < n;i++){
			if(base[i] != spin[i]){
				base[i] = !base[i];
				base[i+2] = !base[i+2];
			}
		}
		if(Arrays.equals(base, spin)){
			out.println("Yes");
		}else{
			out.println("No");
		}
	}
	
	public static int sumFenwick(int[] ft, int i)
	{
		int sum = 0;
		for(i++;i > 0;i -= i&-i)sum += ft[i];
		return sum;
	}
	
	public static void addFenwick(int[] ft, int i, int v)
	{
		if(v == 0 || i < 0)return;
		int n = ft.length;
		for(i++;i < n;i += i&-i)ft[i] += v;
	}

	
	public static void main(String[] args) throws Exception
	{
		long S = System.currentTimeMillis();
		is = INPUT.isEmpty() ? System.in : new ByteArrayInputStream(INPUT.getBytes());
		out = new PrintWriter(System.out);
		
		solve();
		out.flush();
		long G = System.currentTimeMillis();
		tr(G-S+"ms");
	}
	
	private static boolean eof()
	{
		if(lenbuf == -1)return true;
		int lptr = ptrbuf;
		while(lptr < lenbuf)if(!isSpaceChar(inbuf[lptr++]))return false;
		
		try {
			is.mark(1000);
			while(true){
				int b = is.read();
				if(b == -1){
					is.reset();
					return true;
				}else if(!isSpaceChar(b)){
					is.reset();
					return false;
				}
			}
		} catch (IOException e) {
			return true;
		}
	}
	
	private static byte[] inbuf = new byte[1024];
	static int lenbuf = 0, ptrbuf = 0;
	
	private static int readByte()
	{
		if(lenbuf == -1)throw new InputMismatchException();
		if(ptrbuf >= lenbuf){
			ptrbuf = 0;
			try { lenbuf = is.read(inbuf); } catch (IOException e) { throw new InputMismatchException(); }
			if(lenbuf <= 0)return -1;
		}
		return inbuf[ptrbuf++];
	}
	
	private static boolean isSpaceChar(int c) { return !(c >= 33 && c <= 126); }
//	private static boolean isSpaceChar(int c) { return !(c >= 32 && c <= 126); }
	private static int skip() { int b; while((b = readByte()) != -1 && isSpaceChar(b)); return b; }
	
	private static double nd() { return Double.parseDouble(ns()); }
	private static char nc() { return (char)skip(); }
	
	private static String ns()
	{
		int b = skip();
		StringBuilder sb = new StringBuilder();
		while(!(isSpaceChar(b))){
			sb.appendCodePoint(b);
			b = readByte();
		}
		return sb.toString();
	}
	
	private static char[] ns(int n)
	{
		char[] buf = new char[n];
		int b = skip(), p = 0;
		while(p < n && !(isSpaceChar(b))){
			buf[p++] = (char)b;
			b = readByte();
		}
		return n == p ? buf : Arrays.copyOf(buf, p);
	}
	
	private static char[][] nm(int n, int m)
	{
		char[][] map = new char[n][];
		for(int i = 0;i < n;i++)map[i] = ns(m);
		return map;
	}
	
	private static int[] na(int n)
	{
		int[] a = new int[n];
		for(int i = 0;i < n;i++)a[i] = ni();
		return a;
	}
	
	private static int ni()
	{
		int num = 0, b;
		boolean minus = false;
		while((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-'));
		if(b == '-'){
			minus = true;
			b = readByte();
		}
		
		while(true){
			if(b >= '0' && b <= '9'){
				num = num * 10 + (b - '0');
			}else{
				return minus ? -num : num;
			}
			b = readByte();
		}
	}
	
	private static long nl()
	{
		long num = 0;
		int b;
		boolean minus = false;
		while((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-'));
		if(b == '-'){
			minus = true;
			b = readByte();
		}
		
		while(true){
			if(b >= '0' && b <= '9'){
				num = num * 10 + (b - '0');
			}else{
				return minus ? -num : num;
			}
			b = readByte();
		}
	}
	
	private static void tr(Object... o) { if(INPUT.length() != 0)System.out.println(Arrays.deepToString(o)); }
}