{"trustable":true,"prependHtml":"\u003cstyle type\u003d\u0027text/css\u0027\u003e\n .input, .output {\n border: 1px solid #888888;\n }\n .output {\n margin-bottom: 1em;\n position: relative;\n top: -1px;\n }\n .output pre, .input pre {\n background-color: #EFEFEF;\n line-height: 1.25em;\n margin: 0;\n padding: 0.25em;\n }\n \u003c/style\u003e\n \u003clink rel\u003d\"stylesheet\" href\u003d\"//codeforces.org/s/96598/css/problem-statement.css\" type\u003d\"text/css\" /\u003e\n\u003cscript\u003e\n window.katexOptions \u003d {\n delimiters: [\n {left: \u0027$$$$$$\u0027, right: \u0027$$$$$$\u0027, display: true},\n {left: \u0027$$$\u0027, right: \u0027$$$\u0027, display: false},\n {left: \u0027$$\u0027, right: \u0027$$\u0027, display: true},\n {left: \u0027$\u0027, right: \u0027$\u0027, display: false}\n ]\n };\n\u003c/script\u003e\n","sections":[{"title":"","value":{"format":"HTML","content":"\u003cp\u003eThe Dogeforces company has $$$k$$$ employees. Each employee, except for lower-level employees, has at least $$$2$$$ subordinates. Lower-level employees have no subordinates. Each employee, except for the head of the company, has exactly one direct supervisor. The head of the company is a direct or indirect supervisor of all employees. It is known that in Dogeforces, each supervisor receives a salary strictly more than all his subordinates.\u003c/p\u003e\u003cp\u003eThe full structure of the company is a secret, but you know the number of lower-level employees and for each pair of lower-level employees, the salary of their common supervisor is known (if there are several such supervisors, then the supervisor with the minimum salary). You have to restore the structure of the company.\u003c/p\u003e"}},{"title":"Input","value":{"format":"HTML","content":"\u003cp\u003eThe first line contains a single integer $$$n$$$ ($$$2 \\le n \\le 500$$$) — the number of lower-level employees.\u003c/p\u003e\u003cp\u003eThis is followed by $$$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} \u003d a_{j,i}$$$. Note that $$$a_{i,i}$$$ is equal to the salary of the $$$i$$$-th employee.\u003c/p\u003e"}},{"title":"Output","value":{"format":"HTML","content":"\u003cp\u003eIn the first line, print a single integer $$$k$$$ — the number of employees in the company.\u003c/p\u003e\u003cp\u003eIn the second line, print $$$k$$$ integers $$$c_1, c_2, \\dots, c_k$$$, where $$$c_i$$$ is the salary of the employee with the number $$$i$$$.\u003c/p\u003e\u003cp\u003eIn the third line, print a single integer $$$r$$$ — the number of the employee who is the head of the company.\u003c/p\u003e\u003cp\u003eIn the following $$$k-1$$$ lines, print two integers $$$v$$$ and $$$u$$$ ($$$1 \\le v, u \\le k$$$) — the number of the employee and his direct supervisor.\u003c/p\u003e\u003cp\u003eNote that the lower-level employees have numbers from $$$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.\u003c/p\u003e"}},{"title":"Examples","value":{"format":"HTML","content":"\u003ctable class\u003d\u0027vjudge_sample\u0027\u003e\n\u003cthead\u003e\n \u003ctr\u003e\n \u003cth\u003eInput\u003c/th\u003e\n \u003cth\u003eOutput\u003c/th\u003e\n \u003c/tr\u003e\n\u003c/thead\u003e\n\u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd\u003e\u003cpre\u003e3\n2 5 7\n5 1 7\n7 7 4\n\u003c/pre\u003e\u003c/td\u003e\n \u003ctd\u003e\u003cpre\u003e5\n2 1 4 7 5 \n4\n1 5\n2 5\n5 4\n3 4\n\u003c/pre\u003e\u003c/td\u003e\n \u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\n"}},{"title":"Note","value":{"format":"HTML","content":"\u003cp\u003eOne of the possible structures in the first example: \u003cimg class\u003d\"tex-graphics\" src\u003d\"CDN_BASE_URL/3eeb1b1fd47b49f2303c05fb4e31df40?v\u003d1726251571\" style\u003d\"max-width: 100.0%;max-height: 100.0%;\"\u003e\u003c/p\u003e"}}]}