Problem: Given are two sequences A and B, both of length N. A and B are each sorted in the ascending order. Check if it is possible to reorder the terms of B so that for each i (1 \leq i \leq N) A_i \neq B_i holds, and if it is possible, output any of the reorderings that achieve it.

Constraints

* 1\leq N \leq 2 \times 10^5
* 1\leq A_i,B_i \leq N
* A and B are each sorted in the ascending order.
* All values in input are integers.

Input

Input is given from Standard Input in the following format:


N
A_1 A_2 \cdots A_N
B_1 B_2 \cdots B_N


Output

If there exist no reorderings that satisfy the condition, print `No`.

If there exists a reordering that satisfies the condition, print `Yes` on the first line. After that, print a reordering of B on the second line, separating terms with a whitespace.

If there are multiple reorderings that satisfy the condition, you can print any of them.

Examples

Input

6
1 1 1 2 2 3
1 1 1 2 2 3


Output

Yes
2 2 3 1 1 1


Input

3
1 1 2
1 1 3


Output

No


Input

4
1 1 2 3
1 2 3 3


Output

Yes
3 3 1 2

Solution (in JAVA):

Solution:
import java.io.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.util.Arrays;
import java.nio.ByteBuffer;
import java.nio.charset.Charset;
import java.util.NoSuchElementException;
import java.io.OutputStream;
import java.nio.CharBuffer;
import java.io.IOException;
import java.nio.charset.CharsetDecoder;
import java.lang.reflect.Field;
import java.nio.charset.StandardCharsets;
import java.io.UncheckedIOException;
import java.security.AccessControlException;
import java.io.Writer;
import java.io.InputStream;

/**
 * Built using CHelper reloaded plug-in
 * Actual solution is at the top
 *
 * @author mikit
 */
public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        LightScanner2 in = new LightScanner2(inputStream);
        LightWriter2 out = new LightWriter2(outputStream);
        FContrast solver = new FContrast();
        solver.solve(1, in, out);
        out.close();
    }

    static class FContrast {
        public void solve(int testNumber, LightScanner2 in, LightWriter2 out) {
            int n = in.ints();
            int[] a = in.ints(n), b = in.ints(n);
            int[] cntA = new int[n + 1];
            int[] cntB = new int[n + 1];
            for (int i = 0; i < n; i++) {
                cntA[a[i]]++;
                cntB[b[i]]++;
            }
            long begin = System.currentTimeMillis();

            int[] diffs = Arrays.copyOf(cntA, 2 * n);
            System.arraycopy(cntB, 0, diffs, n, n);
            IntroSort.sort(diffs);
            for (int d = Math.max(0, n / 2 - 10); d < Math.min(n, n / 2 + 10); d++) {
                int[] c = test(n, a, b, d);
                if (c == null) continue;
                out.yesln().ans(c).ln();
                return;
            }
            int cur = 0;
            while (cur < 2 * n && diffs[cur] <= 300) cur++;
            for (int i = 0; cur + i < 2 * n && i < 300; i++) {
                int d = diffs[cur + i];
                int[] c = test(n, a, b, d);
                if (c == null) c = test(n, a, b, -d);
                if (c == null) continue;
                out.yesln().ans(c).ln();
                return;
            }

            int d = 0;
            while (System.currentTimeMillis() - begin < 1800) {
                for (int pp = 0; pp < 100; pp++) {
                    int[] c = test(n, a, b, d);
                    if (c == null) c = test(n, a, b, -d);
                    if (c == null) continue;
                    out.yesln().ans(c).ln();
                    d++;
                }
            }
            out.noln();
        }

        private static int[] test(int n, int[] a, int[] b, int d) {
            d = (d % n + n) % n;
            int[] c = new int[n];
            for (int i = 0; i < n; i++) {
                c[(i + d) % n] = b[i];
            }
            for (int i = 0; i < n; i++) if (a[i] == c[i]) return null;
            return c;
        }

    }

    static abstract class LightScannerAdapter implements AutoCloseable {
        public abstract String string();

        public int ints() {
            return Integer.parseInt(string());
        }

        public final int[] ints(int length) {
            int[] res = new int[length];
            Arrays.setAll(res, ignored -> ints());
            return res;
        }

        public abstract void close();

    }

    static class IntroSort {
        private static int INSERTIONSORT_THRESHOLD = 16;

        private IntroSort() {
        }

        static void sort(int[] a, int low, int high, int maxDepth) {
            while (high - low > INSERTIONSORT_THRESHOLD) {
                if (maxDepth-- == 0) {
                    HeapSort.sort(a, low, high);
                    return;
                }
                int cut = QuickSort.step(a, low, high);
                sort(a, cut, high, maxDepth);
                high = cut;
            }
            InsertionSort.sort(a, low, high);
        }

        public static void sort(int[] a) {
            if (a.length <= INSERTIONSORT_THRESHOLD) {
                InsertionSort.sort(a, 0, a.length);
            } else {
                sort(a, 0, a.length, 2 * BitMath.msb(a.length));
            }
        }

    }

    static class InsertionSort {
        private InsertionSort() {
        }

        static void sort(int[] a, int low, int high) {
            for (int i = low; i < high; i++) {
                for (int j = i; j > low && a[j - 1] > a[j]; j--) {
                    ArrayUtil.swap(a, j - 1, j);
                }
            }
        }

    }

    static class QuickSort {
        private QuickSort() {
        }

        private static void med(int[] a, int low, int x, int y, int z) {
            if (a[z] < a[x]) {
                ArrayUtil.swap(a, low, x);
            } else if (a[y] < a[z]) {
                ArrayUtil.swap(a, low, y);
            } else {
                ArrayUtil.swap(a, low, z);
            }
        }

        static int step(int[] a, int low, int high) {
            int x = low + 1, y = low + (high - low) / 2, z = high - 1;
            if (a[x] < a[y]) {
                med(a, low, x, y, z);
            } else {
                med(a, low, y, x, z);
            }

            int lb = low + 1, ub = high;
            while (true) {
                while (a[lb] < a[low]) {
                    lb++;
                }
                ub--;
                while (a[low] < a[ub]) {
                    ub--;
                }
                if (lb >= ub) {
                    return lb;
                }
                ArrayUtil.swap(a, lb, ub);
                lb++;
            }
        }

    }

    static final class BitMath {
        private BitMath() {
        }

        public static int count(int v) {
            return Integer.bitCount(v);
        }

        public static int msb(int v) {
            if (v == 0) {
                throw new IllegalArgumentException("Bit not found");
            }
            v |= (v >> 1);
            v |= (v >> 2);
            v |= (v >> 4);
            v |= (v >> 8);
            v |= (v >> 16);
            return count(v) - 1;
        }

    }

    static class LightWriter2 implements AutoCloseable {
        private static final int BUF_SIZE = 1024 * 1024;
        private static final int BUF_THRESHOLD = 64 * 1024;
        private final OutputStream out;
        private final byte[] buf = new byte[BUF_SIZE];
        private int ptr;
        private final Field fastStringAccess;
        private boolean autoflush = false;
        private boolean breaked = true;
        private LightWriter2.BoolLabel boolLabel = LightWriter2.BoolLabel.YES_NO_FIRST_UP;

        public LightWriter2(OutputStream out) {
            this.out = out;
            Field f;
            try {
                f = String.class.getDeclaredField("value");
                f.setAccessible(true);
                if (f.getType() != byte[].class) f = null;
            } catch (ReflectiveOperationException | AccessControlException ignored) {
                f = null;
            }
            this.fastStringAccess = f;
        }

        public LightWriter2(Writer out) {
            this.out = new LightWriter2.WriterOutputStream(out);
            this.fastStringAccess = null;
        }

        private void allocate(int n) {
            if (ptr + n <= BUF_SIZE) return;
            try {
                out.write(buf, 0, ptr);
                ptr = 0;
            } catch (IOException ex) {
                throw new UncheckedIOException(ex);
            }
            if (BUF_SIZE < n) throw new IllegalArgumentException("Internal buffer exceeded");
        }

        public void close() {
            try {
                out.write(buf, 0, ptr);
                ptr = 0;
                out.flush();
                out.close();
            } catch (IOException ex) {
                throw new UncheckedIOException(ex);
            }
        }

        public LightWriter2 print(char c) {
            allocate(1);
            buf[ptr++] = (byte) c;
            breaked = false;
            return this;
        }

        public LightWriter2 print(String s) {
            byte[] bytes;
            if (this.fastStringAccess == null) bytes = s.getBytes();
            else {
                try {
                    bytes = (byte[]) fastStringAccess.get(s);
                } catch (IllegalAccessException ignored) {
                    bytes = s.getBytes();
                }
            }
            int n = bytes.length;
            if (n <= BUF_THRESHOLD) {
                allocate(n);
                System.arraycopy(bytes, 0, buf, ptr, n);
                ptr += n;
                return this;
            }
            try {
                out.write(buf, 0, ptr);
                ptr = 0;
                out.write(bytes);
                out.flush();
            } catch (IOException ex) {
                throw new UncheckedIOException(ex);
            }
            return this;
        }

        public LightWriter2 ans(String s) {
            if (!breaked) {
                print(' ');
            }
            breaked = false;
            return print(s);
        }

        private int print(long l) {
            if (l == 0) {
                print('0');
                return 1;
            } else if (l < 0) {
                print('-');
                l = -l;
            }
            int n = 0;
            long t = l;
            while (t > 0) {
                t /= 10;
                n++;
            }
            allocate(n);
            for (int i = 1; i <= n; i++) {
                buf[ptr + n - i] = (byte) (l % 10 + '0');
                l /= 10;
            }
            ptr += n;
            return n;
        }

        public LightWriter2 ans(int i) {
            if (!breaked) {
                print(' ');
            }
            breaked = false;
            print(i);
            return this;
        }

        public LightWriter2 ans(boolean b) {
            return ans(boolLabel.transfer(b));
        }

        public LightWriter2 yesln() {
            return ans(true).ln();
        }

        public LightWriter2 noln() {
            return ans(false).ln();
        }

        public LightWriter2 ans(int... n) {
            for (int n1 : n) {
                ans(n1);
            }
            return this;
        }

        public LightWriter2 ln() {
            print(System.lineSeparator());
            breaked = true;
            if (autoflush) {
                try {
                    out.flush();
                } catch (IOException ex) {
                    throw new UncheckedIOException(ex);
                }
            }
            return this;
        }

        public enum BoolLabel {
            YES_NO_FIRST_UP("Yes", "No"),
            YES_NO_ALL_UP("YES", "NO"),
            YES_NO_ALL_DOWN("yes", "no"),
            Y_N_ALL_UP("Y", "N"),
            POSSIBLE_IMPOSSIBLE_FIRST_UP("Possible", "Impossible"),
            POSSIBLE_IMPOSSIBLE_ALL_UP("POSSIBLE", "IMPOSSIBLE"),
            POSSIBLE_IMPOSSIBLE_ALL_DOWN("possible", "impossible"),
            FIRST_SECOND_FIRST_UP("First", "Second"),
            FIRST_SECOND_ALL_UP("FIRST", "SECOND"),
            FIRST_SECOND_ALL_DOWN("first", "second"),
            ALICE_BOB_FIRST_UP("Alice", "Bob"),
            ALICE_BOB_ALL_UP("ALICE", "BOB"),
            ALICE_BOB_ALL_DOWN("alice", "bob"),
            ;
            private final String positive;
            private final String negative;

            BoolLabel(String positive, String negative) {
                this.positive = positive;
                this.negative = negative;
            }

            private String transfer(boolean f) {
                return f ? positive : negative;
            }

        }

        private static class WriterOutputStream extends OutputStream {
            final Writer writer;
            final CharsetDecoder decoder;

            WriterOutputStream(Writer writer) {
                this.writer = writer;
                this.decoder = StandardCharsets.UTF_8.newDecoder();
            }

            public void write(int b) throws IOException {
                writer.write(b);
            }

            public void write(byte[] b) throws IOException {
                writer.write(decoder.decode(ByteBuffer.wrap(b)).array());
            }

            public void write(byte[] b, int off, int len) throws IOException {
                writer.write(decoder.decode(ByteBuffer.wrap(b, off, len)).array());
            }

            public void flush() throws IOException {
                writer.flush();
            }

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

        }

    }

    static final class ArrayUtil {
        private ArrayUtil() {
        }

        public static void swap(int[] a, int x, int y) {
            int t = a[x];
            a[x] = a[y];
            a[y] = t;
        }

    }

    static class HeapSort {
        private HeapSort() {
        }

        private static void heapfy(int[] a, int low, int high, int i, int val) {
            int child = 2 * i - low + 1;
            while (child < high) {
                if (child + 1 < high && a[child] < a[child + 1]) {
                    child++;
                }
                if (val >= a[child]) {
                    break;
                }
                a[i] = a[child];
                i = child;
                child = 2 * i - low + 1;
            }
            a[i] = val;
        }

        static void sort(int[] a, int low, int high) {
            for (int p = (high + low) / 2 - 1; p >= low; p--) {
                heapfy(a, low, high, p, a[p]);
            }
            while (high > low) {
                high--;
                int pval = a[high];
                a[high] = a[low];
                heapfy(a, low, high, low, pval);
            }
        }

    }

    static class LightScanner2 extends LightScannerAdapter {
        private static final int BUF_SIZE = 1024 * 1024;
        private final InputStream stream;
        private final StringBuilder builder = new StringBuilder();
        private final byte[] buf = new byte[BUF_SIZE];
        private int ptr;
        private int len;

        public LightScanner2(InputStream stream) {
            this.stream = stream;
        }

        private int read() {
            if (ptr < len) return buf[ptr++];
            try {
                ptr = 0;
                len = stream.read(buf);
            } catch (IOException ex) {
                throw new UncheckedIOException(ex);
            }
            if (len == -1) return -1;
            return buf[ptr++];
        }

        private void skip() {
            int b;
            while (isTokenSeparator(b = read()) && b != -1) ;
            if (b == -1) throw new NoSuchElementException("EOF");
            ptr--;
        }

        private void loadToken() {
            builder.setLength(0);
            skip();
            for (int b = read(); !isTokenSeparator(b); b = read()) {
                builder.appendCodePoint(b);
            }
        }

        public String string() {
            loadToken();
            return builder.toString();
        }

        public int ints() {
            long x = longs();
            if (x < Integer.MIN_VALUE || Integer.MAX_VALUE < x) throw new NumberFormatException("Overflow");
            return (int) x;
        }

        public long longs() {
            skip();
            int b = read();
            boolean negate;
            if (b == '-') {
                negate = true;
                b = read();
            } else negate = false;
            long x = 0;
            for (; !isTokenSeparator(b); b = read()) {
                if ('0' <= b && b <= '9') x = x * 10 + b - '0';
                else throw new NumberFormatException("Unexpected character '" + b + "'");
            }
            return negate ? -x : x;
        }

        public void close() {
            try {
                stream.close();
            } catch (IOException e) {
                throw new UncheckedIOException(e);
            }
        }

        private static boolean isTokenSeparator(int b) {
            return b < 33 || 126 < b;
        }

    }
}