Magnus decided to play a classic chess game. Though what he saw in his locker shocked him! His favourite chessboard got broken into 4 pieces, each of size n by n, n is always odd. And what's even worse, some squares were of wrong color. j-th square of the i-th row of k-th piece of the board has color ak, i, j; 1 being black and 0 being white. 

Now Magnus wants to change color of some squares in such a way that he recolors minimum number of squares and obtained pieces form a valid chessboard. Every square has its color different to each of the neightbouring by side squares in a valid board. Its size should be 2n by 2n. You are allowed to move pieces but not allowed to rotate or flip them.

Input

The first line contains odd integer n (1 ≤ n ≤ 100) — the size of all pieces of the board. 

Then 4 segments follow, each describes one piece of the board. Each consists of n lines of n characters; j-th one of i-th line is equal to 1 if the square is black initially and 0 otherwise. Segments are separated by an empty line.

Output

Print one number — minimum number of squares Magnus should recolor to be able to obtain a valid chessboard.

Examples

Input

1
0

0

1

0


Output

1


Input

3
101
010
101

101
000
101

010
101
011

010
101
010


Output

2
import java.io.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.OutputStream;
import java.io.PrintWriter;
import java.io.BufferedWriter;
import java.util.InputMismatchException;
import java.io.IOException;
import java.io.Writer;
import java.io.OutputStreamWriter;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 */
public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        InputReader in = new InputReader(inputStream);
        OutputWriter out = new OutputWriter(outputStream);
        EChessboard solver = new EChessboard();
        solver.solve(1, in, out);
        out.close();
    }

    static class EChessboard {
        int IINF = (int) 1e9 + 331;

        public void solve(int testNumber, InputReader in, OutputWriter out) {
            int ntc = 1;
//        ntc = in.nextInt();
            while ((ntc--) > 0) {
                int n = in.nextInt();
                _C.Pair<Integer, Integer>[] pairs = new _C.Pair[4];
                for (int i = 0; i < 4; i++) {
                    pairs[i] = nextMatrix(in, n);
                }
                int minCost = +IINF;
                int cost = 0;
                for (int i = 0; i < 4; i++) {
                    for (int j = 0; j < 4; j++) {
                        if (j == i) {
                            continue;
                        }
                        cost = pairs[i].f;
                        cost += pairs[j].f;
                        for (int k = 0; k < 4; k++) {
                            if (k != i && k != j) {
                                cost += pairs[k].s;
                            }
                        }
                        minCost = _F.min(minCost, cost);
                    }
                }
                out.println(minCost);
            }
        }

        public _C.Pair<Integer, Integer> nextMatrix(InputReader in, int n) {
            int bc = 0, wc = 0, bs = 0, ws = 0;
            for (int i = 0; i < n; i++) {
                if (i % 2 == 0) {
                    bs = 1;
                    ws = 0;
                } else {
                    bs = 0;
                    ws = 1;
                }
                for (int j = 0; j < n; j++) {
                    int x = in.nextCharacter() == '1' ? 1 : 0;
                    if (x != bs) {
                        bc++;
                    }
                    if (x != ws) {
                        wc++;
                    }
                    bs ^= 1;
                    ws ^= 1;
                }
            }
            return new _C.Pair<>(bc, wc);
        }

    }

    static class InputReader {
        private InputStream stream;
        private byte[] buf = new byte[1024];
        private int curChar;
        private int numChars;
        private InputReader.SpaceCharFilter filter;

        public InputReader(InputStream stream) {
            this.stream = stream;
        }

        public int read() {
            if (numChars == -1) {
                throw new InputMismatchException();
            }
            if (curChar >= numChars) {
                curChar = 0;
                try {
                    numChars = stream.read(buf);
                } catch (IOException e) {
                    throw new InputMismatchException();
                }
                if (numChars <= 0) {
                    return -1;
                }
            }
            return buf[curChar++];
        }

        public int nextInt() {
            int c = read();
            while (isSpaceChar(c)) {
                c = read();
            }
            int sgn = 1;
            if (c == '-') {
                sgn = -1;
                c = read();
            }
            int res = 0;
            do {
                if (c < '0' || c > '9') {
                    throw new InputMismatchException();
                }
                res *= 10;
                res += c - '0';
                c = read();
            } while (!isSpaceChar(c));
            return res * sgn;
        }

        public boolean isSpaceChar(int c) {
            if (filter != null) {
                return filter.isSpaceChar(c);
            }
            return isWhitespace(c);
        }

        public static boolean isWhitespace(int c) {
            return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
        }

        public char nextCharacter() {
            int c = read();
            while (isSpaceChar(c)) {
                c = read();
            }
            return (char) c;
        }

        public interface SpaceCharFilter {
            public boolean isSpaceChar(int ch);

        }

    }

    static class _F {
        public static <T extends Comparable<T>> T min(T... list) {
            T candidate = list[0];
            for (T i : list) {
                if (candidate.compareTo(i) > 0) {
                    candidate = i;
                }
            }
            return candidate;
        }

    }

    static class _C {
        static public class Pair<F extends Comparable<F>, S extends Comparable<S>> implements Comparable<_C.Pair<F, S>> {
            public F f;
            public S s;

            public Pair(F f, S s) {
                this.f = f;
                this.s = s;
            }

            public int compareTo(_C.Pair<F, S> o) {
                int t = f.compareTo(o.f);
                if (t == 0) return s.compareTo(o.s);
                return t;
            }

            public int hashCode() {
                return (31 + f.hashCode()) * 31 + s.hashCode();
            }

            public boolean equals(Object o) {
                if (!(o instanceof _C.Pair)) return false;
                if (o == this) return true;
                _C.Pair p = (_C.Pair) o;
                return f.equals(p.f) && s.equals(p.s);
            }

            public String toString() {
                return "{" + f + ", " + s + "}";
            }

        }

    }

    static class OutputWriter {
        private final PrintWriter writer;

        public OutputWriter(OutputStream outputStream) {
            writer = new PrintWriter(new BufferedWriter(new OutputStreamWriter(outputStream)));
        }

        public OutputWriter(Writer writer) {
            this.writer = new PrintWriter(writer);
        }

        public void close() {
            writer.close();
        }

        public void println(long i) {
            writer.println(i);
        }

    }
}

