Round 349 B Div1 : 666B - World Tour.
The Idea of problem is fixing two middle cities!
But I solved the problem by this Idea :
Consider that the answer's cities are a, b, c, d and a < b < c < d
---- dp[ k ][ i ] = the maximum length with k cities so that k'th city is i(labels are increasing!).
---- We can update dp with O(n ^ 2) [ dp[ k ][ i ] = max(j < i : dp[ k — 1 ][ j ] + d[ j ][ i ]) ]

We shuffle the labels of cities while the labels of answer's cities become increasing!
The mathematical expectation of the above algorithm is (4! * 4 * N ^ 2) :))
My implementation : 17588529.
We can have a harder problem with five cities : (5! * 5 * N ^ 2)