Standing Out from the Herd

Just like people, cows like to feel they are special in some way. Farmer John's cows all come from the same breed and look alike, so they measure uniqueness by their names.

Each cow's name contains a number of substrings. For example, "amy" has substrings {a, m, y, am, my, amy}, and "tommy" has substrings {t, o, m, y, to, om, mm, my, tom, omm, mmy, tomm, ommy, tommy}.

The uniqueness factor of a name is the number of distinct substrings of that name that appear in no other cow's name. If amy were alone in a herd, her uniqueness factor would be 6. If tommy were alone, his would be 14. With both cows in the same herd, amy's factor is 3 and tommy's factor is 11.

Given a herd of cows, compute each cow's uniqueness factor.

The first line contains $N$ ($1 \le N \le 10^5$). Each of the next $N$ lines contains the name of one cow in the herd. Each name contains only lowercase letters a to z. The total length of all names does not exceed $10^5$.

Print $N$ lines. Each line holds the uniqueness factor of one cow, in the order the names are given in the input.