Problem: You are given an array a of n integers.

You want to make all elements of a equal to zero by doing the following operation exactly three times:

  * Select a segment, for each number in this segment we can add a multiple of len to it, where len is the length of this segment (added integers can be different). 



It can be proven that it is always possible to make all elements of a equal to zero.

Input

The first line contains one integer n (1 ≤ n ≤ 100 000): the number of elements of the array.

The second line contains n elements of an array a separated by spaces: a_1, a_2, ..., a_n (-10^9 ≤ a_i ≤ 10^9).

Output

The output should contain six lines representing three operations.

For each operation, print two lines:

  * The first line contains two integers l, r (1 ≤ l ≤ r ≤ n): the bounds of the selected segment.

  * The second line contains r-l+1 integers b_l, b_{l+1}, ..., b_r (-10^{18} ≤ b_i ≤ 10^{18}): the numbers to add to a_l, a_{l+1}, …, a_r, respectively; b_i should be divisible by r - l + 1.

Example

Input


4
1 3 2 4


Output


1 1 
-1
3 4
4 2
2 4
-3 -6 -6

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.util.Objects;
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);
        AMultiplesOfLength solver = new AMultiplesOfLength();
        solver.solve(1, in, out);
        out.close();
    }

    static class AMultiplesOfLength {
        public void solve(int testNumber, LightScanner2 in, LightWriter2 out) {
            int n = in.ints();
            long[] a = in.longs(n);
            if (n == 1) {
                out.ans(1).ans(1).ln().ans(-a[0]).ln();
                out.ans(1).ans(1).ln().ans(0).ln();
                out.ans(1).ans(1).ln().ans(0).ln();
                return;
            } else if (n == 2) {
                out.ans(1).ans(1).ln().ans(-a[0]).ln();
                out.ans(2).ans(2).ln().ans(-a[1]).ln();
                out.ans(1).ans(1).ln().ans(0).ln();
                return;
            }
            Vec3l sol = LongEuclidSolver.solve(n, n - 1);
            if (sol.z != 1) throw new RuntimeException();
            long[] p1 = new long[n], p2 = new long[n];
            for (int i = 0; i < n; i++) {
                p1[i] = -n * a[i] * sol.x;
                p2[i] = -(n - 1L) * a[i] * sol.y;
            }
            // 1
            out.ans(1).ans(n).ln();
            for (int i = 0; i < n - 1; i++) {
                out.ans(p1[i]);
                a[i] += p1[i];
            }
            out.ans(0).ln();
            // 2
            out.ans(1).ans(n - 1).ln();
            for (int i = 0; i < n - 1; i++) {
                out.ans(p2[i]);
                a[i] += p2[i];
            }
            out.ln();
            //3
            out.ans(n).ans(n).ln().ans(-a[n - 1]).ln();
            a[n - 1] = 0;
        /*
        for (int i = 0; i < n; i++) {
            if (a[i] != 0) throw new RuntimeException();
        }*/
        }

    }

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

        public long longs() {
            return Long.parseLong(string());
        }

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

        public abstract void close();

    }

    static class LongEuclidSolver {
        private LongEuclidSolver() {
        }

        public static Vec3l solve(long a, long b) {
            LongEuclidSolver.ReferenceLong p = new LongEuclidSolver.ReferenceLong(), q = new LongEuclidSolver.ReferenceLong();
            long d = solve(a, b, p, q);
            return new Vec3l(p.val, q.val, d);
        }

        private static long solve(long a, long b, LongEuclidSolver.ReferenceLong p, LongEuclidSolver.ReferenceLong q) {
            if (b == 0) {
                p.val = 1;
                q.val = 0;
                return a;
            } else {
                long d = solve(b, a % b, q, p);
                q.val -= (a / b) * p.val;
                return d;
            }
        }

        private static class ReferenceLong {
            private long val;

        }

    }

    static class Vec3l implements Comparable<Vec3l> {
        public long x;
        public long y;
        public long z;

        public Vec3l(long x, long y, long z) {
            this.x = x;
            this.y = y;
            this.z = z;
        }

        public boolean equals(Object o) {
            if (this == o) return true;
            if (o == null || getClass() != o.getClass()) return false;
            Vec3i vec3i = (Vec3i) o;
            return x == vec3i.x &&
                    y == vec3i.y &&
                    z == vec3i.z;
        }

        public int hashCode() {
            return Objects.hash(x, y, z);
        }

        public String toString() {
            return "(" + x + ", " + y + ", " + z + ")";
        }

        public int compareTo(Vec3l o) {
            if (x == o.x) {
                if (y == o.y) {
                    return Long.compare(z, o.z);
                }
                return Long.compare(y, o.z);
            }
            return Long.compare(x, o.x);
        }

    }

    static class LightScanner2 extends LightScannerAdapter {
        private static final int BUF_SIZE = 32 * 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;
        }

    }

    static class Vec3i implements Comparable<Vec3i> {
        public int x;
        public int y;
        public int z;

        public Vec3i(int x, int y, int z) {
            this.x = x;
            this.y = y;
            this.z = z;
        }

        public boolean equals(Object o) {
            if (this == o) return true;
            if (o == null || getClass() != o.getClass()) return false;
            Vec3i vec3i = (Vec3i) o;
            return x == vec3i.x &&
                    y == vec3i.y &&
                    z == vec3i.z;
        }

        public int hashCode() {
            return Objects.hash(x, y, z);
        }

        public String toString() {
            return "(" + x + ", " + y + ", " + z + ")";
        }

        public int compareTo(Vec3i o) {
            if (x == o.x) {
                if (y == o.y) {
                    return Integer.compare(z, o.z);
                }
                return Integer.compare(y, o.z);
            }
            return Integer.compare(x, o.x);
        }

    }

    static class LightWriter2 implements AutoCloseable {
        private static final int BUF_SIZE = 32 * 1024;
        private static final int BUF_THRESHOLD = 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;

        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(long l) {
            if (!breaked) {
                print(' ');
            }
            breaked = false;
            if (l == 0) return print('0');
            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 this;
        }

        public LightWriter2 ans(int i) {
            if (!breaked) {
                print(' ');
            }
            breaked = false;
            if (i == 0) return print('0');
            if (i < 0) {
                print('-');
                i = -i;
            }
            int n = 0;
            long t = i;
            while (t > 0) {
                t /= 10;
                n++;
            }
            allocate(n);
            for (int j = 1; j <= n; j++) {
                buf[ptr + n - j] = (byte) (i % 10 + '0');
                i /= 10;
            }
            ptr += n;
            return this;
        }

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

        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();
            }

        }

    }
}