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A. Multiples of Length

time limit per test

1 secondmemory limit per test

256 megabytesinput

standard inputoutput

standard outputYou 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 $$$n$$$ ($$$1 \le n \le 100\,000$$$): the number of elements of the array.

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

Output

The output should contain six lines representing three operations.

For each operation, print two lines:

- The first line contains two integers $$$l$$$, $$$r$$$ ($$$1 \le l \le r \le n$$$): the bounds of the selected segment.
- The second line contains $$$r-l+1$$$ integers $$$b_l, b_{l+1}, \dots, b_r$$$ ($$$-10^{18} \le b_i \le 10^{18}$$$): the numbers to add to $$$a_l, a_{l+1}, \ldots, a_r$$$, 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

Codeforces (c) Copyright 2010-2021 Mike Mirzayanov

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