P7117 Mivik Convolution

The king of grinders grinds through the intestines (doge).

Once upon a time, there was a Mivik who liked convolution. He defines the Mivik convolution of two polynomial functions $f\left(x\right)$ and $g\left(x\right)$ (both only related to $x$) as follows: $$ f\left(x\right)\otimes g\left(x\right)=\sum_{k=0}^{\deg f +\deg g}\max_{i\in [0,\deg f] \land j\in [0,\deg g]\land i+j=k}\left\{\left[x^i\right]f\left(x\right)+\left[x^j\right]g\left(x\right)\right\} x^k $$ Here $\deg f$ denotes the highest degree of $f$, and $\left[x^i\right]f\left(x\right)$ denotes the coefficient of the $x^i$ term in $f\left(x\right)$. Note that Mivik convolution is left-associative, i.e., $a\otimes b\otimes c=(a\otimes b)\otimes c$. Mivik defines a Mivik function as a function that can be written in the form $f\left(x\right)=ax+b$, where $a$ and $b$ are both integers. For example, $f\left(x\right)=-3+2x$ is a Mivik function, while $f\left(x\right)=\frac{1}{x}$ is not. Mivik also defines a function $f\left(x\right)$ to be simple if and only if there exists a sequence $S$ of Mivik functions (of size $\left|S\right|$) such that: $$ f\left(x\right)=S_1\otimes S_2\otimes S_3\otimes\cdots\otimes S_{\left|S\right|}. $$ Now Mivik gives you a polynomial function. Determine whether this function is simple. If it is, also output any possible $S$.

The first line contains a positive integer $n$, representing the number of terms of this polynomial function. The second line contains $n$ integers. From low degree to high degree, they represent the coefficients $f_i$ of this polynomial function. It is guaranteed that the highest-degree coefficient is non-zero.

If this function is not simple, output one line `nice`. Otherwise, first output one line `simple`, then output one line with the size $\left|S\right|$ of the sequence $S$ you construct. In the next $\left|S\right|$ lines, output the sequence $S$ you construct. Each line contains two integers $a$ and $b$, describing a Mivik function $f\left(x\right)=ax+b$.

### Sample Explanation #1 The given function $f\left(x\right)=2+3x+3x^2$ can be obtained from $\left(2x+1\right)\otimes\left(x+1\right)$. ### Constraints **This problem uses bundled testdata.** For all data, $1\le n\le 5\times 10^5$, $-10^8\le f_i\le 10^8$. The detailed limits for each subtask are shown in the table below: | Subtask ID | Score | $n\le$ | |:-:|:-:|:-:| | 1 | 5 | $1$ | | 2 | 5 | $2$ | | 3 | 20 | $20$ | | 4 | 30 | $5000$ | | 5 | 40 | $5\times 10^5$ | **The input and output size of this problem is large. Please use fast I/O.** Translated by ChatGPT 5