Xorability

Consider a tree with $n$ nodes numbered from 1 to $n$ , rooted at 1. Each node $i$ has a natural label $\ell_i$ . Given two nodes $u$ and $v$ , define $X(u, v)$ as the exclusive or (^ in C++) of all the $\ell_i$ in the path from $u$ to $v$ .

Let $L$ be the set of leaves of the tree. Please compute $\sum_{v \in L} X(1, v)$ .

Input

Input consists of several trees, each with the number of nodes $n$ , followed by $\ell_1, \dots, \ell_n$ , followed by $n - 1$ pairs of nodes describing the edges of the tree. Assume $2 \le n \le 10^5$ , and $0 \le l_i \le 10^9$ .

Output

For each tree, print the required sum.

Problem information

Author: Ángel García

Generation: 2026-01-25T11:12:53.826Z