Multiples of Length
Description
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.
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: $a_1, a_2, \dots, a_n$ ($-10^9 \le a_i \le 10^9$).
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 $r - l + 1$.
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 $r - l + 1$.
Samples
4
1 3 2 4
1 1
-1
3 4
4 2
2 4
-3 -6 -6