B"Julia's n friends want to organize a startup in a new country they moved to. They assigned each other numbers from 1 to n according to the jobs they have, from the most front-end tasks to the most back-end ones. They also estimated a matrix c , where c_{ij} = c_{ji} is the average number of messages per month between people doing jobs i and j . Now they want to make a hierarchy tree. It will be a binary tree with each node containing one member of the team. Some member will be selected as a leader of the team and will be contained in the root node. In order for the leader to be able to easily reach any subordinate, for each node v of the tree, the following should apply: all members in its left subtree must have smaller numbers than v , and all members in its right subtree must have larger numbers than v . After the hierarchy tree is settled, people doing jobs i and j will be communicating via the shortest path in the tree between their nodes. Let's denote the length of this path as d_{ij} . Thus, the cost of their communication is c_{ij} cdot d_{ij} . Your task is to find a hierarchy tree that minimizes the total cost of communication over all pairs: sum_{1 <= i < j <= n} c_{ij} cdot d_{ij} . The first line contains an integer n ( 1 <= n <= 200 ) xe2 x80 x93 the number of team members organizing a startup. The next n lines contain n integers each, j -th number in i -th line is c_{ij} -- the estimated number of messages per month between team members i and j ( 0 <= c_{ij} <= 10^9; c_{ij} = c_{ji}; c_{ii} = 0 ). Output a description of a hierarchy tree that minimizes the total cost of communication. To do so, for each team member from 1 to n output the number of the member in its parent node, or 0 for the leader. If there are many optimal trees, output a description of any one of them. The minimal possible total cost i"...