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.BufferedReader;
import java.io.InputStreamReader;
import java.util.*;
import java.util.stream.Collectors;

public class Main {

    public static final BufferedReader br = new BufferedReader(new InputStreamReader(System.in));

    public static void main(String[] args) throws Exception {
        long n = readInt();
        long[] a = readLongArray();
        if(n==1) {
            System.out.println("1 1");
            System.out.println("0");
            System.out.println("1 1");
            System.out.println("0");
            System.out.println("1 1");
            System.out.println(-1*a[0]);
        }
        else {
            System.out.println("1 " + n);
            for (int i = 0; i < n; i++) {
                long k2 = n-a[i];
                long k1n = -1*(1-k2)*n;
                System.out.print(k1n + " ");
            }
            System.out.println();
            System.out.println("2 " + n);
            for (int i = 1; i < n; i++) {
                long k2 = n-a[i];
                long k2n = -1*k2*(n-1);
                System.out.print(k2n+" ");
            }
            long k20 = n-a[0];
            long k1n0 = -1*(1-k20)*n;
            a[0]+=k1n0;
            System.out.println();
            System.out.println("1 1");
            System.out.println(-1*a[0]);
        }
    }

    private static String readString() throws Exception {
        return br.readLine();
    }

    private static int readInt() throws Exception{
        return Integer.parseInt(readString());
    }

    private static long readLong() throws Exception{
        return Long.parseLong(readString());
    }

    private static double readDouble() throws Exception{
        return Double.parseDouble(readString());
    }

    private static String[] readStringArray() throws Exception {
        return br.readLine().split(" ");
    }

    private static List<String> readStringList() throws Exception {
        return Arrays.asList(readStringArray());
    }

    private static List<Integer> readIntList() throws Exception {
        return readStringList().stream().map(s -> Integer.parseInt(s)).collect(Collectors.toList());
    }

    private static int[] readIntArray() throws Exception {
        return readIntList().stream().mapToInt(i -> i).toArray();
    }

    private static List<Long> readLongList() throws Exception {
        return readStringList().stream().map(s -> Long.parseLong(s)).collect(Collectors.toList());
    }

    private static long[] readLongArray() throws Exception {
        return readLongList().stream().mapToLong(i -> i).toArray();
    }

    private static List<Double> readDoubleList() throws Exception {
        return readStringList().stream().map(s -> Double.parseDouble(s)).collect(Collectors.toList());
    }

    private static double[] readDoubleArray() throws Exception {
        return readDoubleList().stream().mapToDouble(i -> i).toArray();
    }
}