Problem Statement

We have a weighted tree with $N$ vertices. The $i$-th edge connects Vertex $u_i$ and Vertex $v_i$ bidirectionally and has a weight $w_i$.

For a pair of vertices $(x,y)$, let us define $\\text{dist}(x,y)$ as follows:

• the XOR of the weights of the edges in the shortest path from $x$ to $y$.

Find $\\text{dist}(i,j)$ for every pair $(i,j)$ such that $1 \\leq i \\lt j \\leq N$, and print the sum of those values modulo $(10^9+7)$.

What is $\\text{ XOR }$?

The bitwise $\\mathrm{XOR}$ of integers $A$ and $B$, $A\\ \\mathrm{XOR}\\ B$, is defined as follows:

• When $A\\ \\mathrm{XOR}\\ B$ is written in base two, the digit in the $2^k$'s place ($k \\geq 0$) is $1$ if exactly one of $A$ and $B$ is $1$, and $0$ otherwise.

For example, we have $3\\ \\mathrm{XOR}\\ 5 = 6$ (in base two: $011\\ \\mathrm{XOR}\\ 101 = 110$).

Constraints

• $2 \\leq N \\leq 2 \\times 10^5$
• $1 \\leq u_i \\lt v_i \\leq N$
• $0 \\leq w_i \\lt 2^{60}$
• The given graph is a tree.
• All values in input are integers.

Input

Input is given from Standard Input in the following format:

$N$ $u_1$ $v_1$ $w_1$ $u_2$ $v_2$ $w_2$ $\\vdots$ $u_{N-1}$ $v_{N-1}$ $w_{N-1}$

Output

Print the sum of $\\text{dist}(i,j)$, modulo $(10^9+7)$.

Sample Input 1

3
1 2 1
1 3 3

Sample Output 1

6

We have $\\text{dist}(1,2)=1,$ $\\text{dist}(1,3)=3,$ and $\\text{dist}(2,3)=2$, for the sum of $6$.

Sample Input 2

5
3 5 2
2 3 2
1 5 1
4 5 13

Sample Output 2

62

Sample Input 3

10
5 7 459221860242673109
6 8 248001948488076933
3 5 371922579800289138
2 5 773108338386747788
6 10 181747352791505823
1 3 803225386673329326
7 8 139939802736535485
9 10 657980865814127926
2 4 146378247587539124

Sample Output 3

241240228

Print the sum modulo $(10^9+7)$.