Weapon Value

A competition with $N$ participants (numbered $1$ through $N$) is taking place in Chefland. There are $N-1$ rounds in the competition; in each round, two arbitrarily chosen contestants battle, one of them loses and drops out of the competition. There are $10$ types of weapons (numbered $1$ through $10$). You are given $N$ strings $S_1, S_2, \ldots, S_N$; for each valid $i$ and $j$, the $j$-th c