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.*;
import java.util.*;

public class Solution {

    private static final String NO = "NO";
    private static final String YES = "YES";
    public static BufferedWriter bw;
    public static FastReader sc;
    private static final int LIMIT = (int) Math.pow(10, 6);

    public static void main(String[] args) throws Exception {
        FastReader sc = new FastReader();
        bw = new BufferedWriter(new OutputStreamWriter(System.out));
//        int t = sc.nextInt();
        int t = 1;
        while (t > 0) {
            t--;
            int n = sc.nextInt();
            long[] a = sc.nextLongArr(n);
            solve(n, a);
//            bw.write(ans + "\n");
        }
        bw.close();
    }

    private static void solve(int n, long[] a) throws IOException {
        bw.write("1 1\n");
        bw.write((a[0] * (-1)) + "\n");
        a[0] = 0;
        if (n == 1) {
            bw.write("1 1\n");
            bw.write(0 + "\n");
            bw.write("1 1\n");
            bw.write(0 + "\n");
            return;
        }
        bw.write(2 + " " + n + "\n");
        update(n, a, 1, n);
        bw.write(1 + " " + n + "\n");
        for (long x : a) {
            bw.write((x * (-1)) + " ");
        }
        bw.write("\n");
    }

    private static void update(int n, long[] a, int l, int r) throws IOException {
        for (int i = l; i < r; i++) {
            long val = val(a[i], n);
            bw.write(val + " ");
            a[i] += val;
        }
        bw.write("\n");
    }

    private static long val(long x, int n) {
        long rem = x % n;
        long m = n - 1;
        return m * rem;
    }


}

class FastReader {
    BufferedReader br;
    StringTokenizer st;

    public FastReader() {
        br = new BufferedReader(new InputStreamReader(System.in));
    }

    public String next() {
        if (st == null || !st.hasMoreTokens()) {
            try {
                st = new StringTokenizer(br.readLine());
            } catch (IOException e) {

            }
        }
        return st.nextToken();
    }

    public int nextInt() {
        return Integer.parseInt(next());
    }

    public int[] nextIntArr(int n) {
        int[] a = new int[n];
        for (int i = 0; i < n; i++) {
            a[i] = nextInt();
        }
        return a;
    }

    public long[] nextLongArr(int n) {
        long[] a = new long[n];
        for (int i = 0; i < n; i++) {
            a[i] = nextLong();
        }
        return a;
    }

    public String[] nextStringArray(int n) {
        String[] a = new String[n];
        for (int i = 0; i < n; i++) {
            a[i] = next();
        }
        return a;
    }

    public long nextLong() {
        return Long.parseLong(next());
    }
}