Shil came across N strings - s₁ , s₂ , s₃ .. s_N . He wants to find out total number of unordered pairs (i, j) such that LCP(s_i , s_j) = k. You have to do thi for every k in [0, L]. Here L = max ( len(s_i) ) and LCP denotes longest common prefix.

INPUT:
First line consists of integer N denoting total number of strings.Next N lines consists of strings s₁ , s₂ , s₃ .. s_N.

OUTPUT:
Print L+1 integers - h₀ , h₁ , h₂, ..., h_L where h_i denotes total number of pairs having LCP value i and L = max ( len(s_i) ).

CONTRAINTS:
1 ≤ N ≤ 10⁵
1≤ Σ len(s_i) ≤ 10⁶
Strings consists of lower case english alphabets ( 'a' - 'z' ) only.