A. Multiples of Length
constructive algorithms; greedy; number theory
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 \(r - l + 1\).