CF1494D.Dogeforces

The Dogeforces company has $k$ employees. Each employee, except for lower-level employees, has at least $2$ subordinates. Lower-level employees have no subordinates. Each employee, except for the head of the company, has exactly one direct supervisor. The head of the company is a direct or indirect supervisor of all employees. It is known that in Dogeforces, each supervisor receives a salary strictly more than all his subordinates.

The full structure of the company is a secret, but you know the number of lower-level employees and for each pair of lower-level employees, the salary of their common supervisor is known (if there are several such supervisors, then the supervisor with the minimum salary). You have to restore the structure of the company.

Dogeforces 公司共有 $k$ 名员工。除基层员工外，每位员工至少有 $2$ 名下属；基层员工没有下属。除公司最高负责人外，每位员工恰好有一位直属上级；公司最高负责人是所有员工的直接或间接上级。已知在 Dogeforces 公司中，每位上级的薪资严格高于其所有下属的薪资。

公司完整的组织结构是保密的，但你知道基层员工的数量，以及每对基层员工的共同上级的薪资（若存在多个共同上级，则取其中薪资最低者）。你需要还原出该公司的组织结构。

The first line contains a single integer $n$ ($2 \le n \le 500$) — the number of lower-level employees.

This is followed by $n$ lines, where $i$-th line contains $n$ integers $a_{i,1}, a_{i,2}, \dots, a_{i,n}$ ($1 \le a_{i,j} \le 5000$) — salary of the common supervisor of employees with numbers $i$ and $j$. It is guaranteed that $a_{i,j} = a_{j,i}$. Note that $a_{i,i}$ is equal to the salary of the $i$-th employee.

第一行包含一个整数 $n$（$2 \le n \le 500$）—— 表示基层员工的数量。

接下来是 $n$ 行，其中第 $i$ 行包含 $n$ 个整数 $a_{i,1}, a_{i,2}, \dots, a_{i,n}$（$1 \le a_{i,j} \le 5000$）—— 表示编号为 $i$ 和 $j$ 的员工的共同直属上司的薪资。保证 $a_{i,j} = a_{j,i}$。注意，$a_{i,i}$ 等于第 $i$ 名员工自身的薪资。

In the first line, print a single integer $k$ — the number of employees in the company.

In the second line, print $k$ integers $c_1, c_2, \dots, c_k$, where $c_i$ is the salary of the employee with the number $i$.

In the third line, print a single integer $r$ — the number of the employee who is the head of the company.

In the following $k-1$ lines, print two integers $v$ and $u$ ($1 \le v, u \le k$) — the number of the employee and his direct supervisor.

Note that the lower-level employees have numbers from $1$ to $n$, and for the rest of the employees, you have to assign numbers from $n+1$ to $k$. If there are several correct company structures, you can print any of them.

第一行，输出一个整数 $k$ —— 公司中员工的总数。

第二行，输出 $k$ 个整数 $c_1, c_2, \dots, c_k$，其中 $c_i$ 表示编号为 $i$ 的员工的工资。

第三行，输出一个整数 $r$ —— 公司最高领导（即公司负责人）的员工编号。

接下来的 $k-1$ 行中，每行输出两个整数 $v$ 和 $u$（$1 \le v, u \le k$），表示员工编号 $v$ 及其直属上级编号 $u$。

注意：底层员工的编号为 $1$ 到 $n$；其余员工的编号需从 $n+1$ 到 $k$ 中分配。若存在多种合法的公司结构，输出任意一种即可。

One of the possible structures in the first example:

第一个示例中的一种可能结构：