You are given a tree consisting of n nodes. You generate an array from the tree by marking nodes one by one.

Initially, when no nodes are marked, a node is equiprobably chosen and marked from the entire tree. 

After that, until all nodes are marked, a node is equiprobably chosen and marked from the set of unmarked nodes with at least one edge to a marked node. 

It can be shown that the process marks all nodes in the tree. 

The final array a is the list of the nodes' labels in order of the time each node was marked.

Find the expected number of inversions in the array that is generated by the tree and the aforementioned process.

The number of inversions in an array a is the number of pairs of indices (i, j) such that i < j and a_i > a_j. For example, the array [4, 1, 3, 2] contains 4 inversions: (1, 2), (1, 3), (1, 4), (3, 4).

Input

The first line contains a single integer n (2 ≤ n ≤ 200) — the number of nodes in the tree.

The next n - 1 lines each contains two integers x and y (1 ≤ x, y ≤ n; x ≠ y), denoting an edge between node x and y.

It's guaranteed that the given edges form a tree.

Output

Output the expected number of inversions in the generated array modulo 10^9+7.

Formally, let M = 10^9+7. It can be shown that the answer can be expressed as an irreducible fraction p/q, where p and q are integers and q not ≡ 0 \pmod{M}. Output the integer equal to p ⋅ q^{-1} mod M. In other words, output such an integer x that 0 ≤ x < M and x ⋅ q ≡ p \pmod{M}.

Examples

Input


3
1 2
1 3


Output


166666669


Input


6
2 1
2 3
6 1
1 4
2 5


Output


500000009


Input


5
1 2
1 3
1 4
2 5


Output


500000007

Note

This is the tree from the first sample:

<image>

For the first sample, the arrays are almost fixed. If node 2 is chosen initially, then the only possible array is [2, 1, 3] (1 inversion). If node 3 is chosen initially, then the only possible array is [3, 1, 2] (2 inversions). If node 1 is chosen initially, the arrays [1, 2, 3] (0 inversions) and [1, 3, 2] (1 inversion) are the only possibilities and equiprobable. In total, the expected number of inversions is 1/3⋅ 1 + 1/3 ⋅ 2 + 1/3 ⋅ (1/2 ⋅ 0 + 1/2 ⋅ 1) = 7/6. 

166666669 ⋅ 6 = 7 \pmod {10^9 + 7}, so the answer is 166666669.

This is the tree from the second sample: 

<image>

This is the tree from the third sample: 

<image>
import bisect
import copy
import decimal
import fractions
import heapq
import itertools
import math
import random
import sys
from collections import Counter, deque,defaultdict
from functools import lru_cache,reduce
from heapq import heappush,heappop,heapify,heappushpop,_heappop_max,_heapify_max
def _heappush_max(heap,item):
    heap.append(item)
    heapq._siftdown_max(heap, 0, len(heap)-1)
def _heappushpop_max(heap, item):
    if heap and item < heap[0]:
        item, heap[0] = heap[0], item
        heapq._siftup_max(heap, 0)
    return item
from math import gcd as GCD
read=sys.stdin.read
readline=sys.stdin.readline
readlines=sys.stdin.readlines

def Extended_Euclid(n,m):
    stack=[]
    while m:
        stack.append((n,m))
        n,m=m,n%m
    if n>=0:
        x,y=1,0
    else:
        x,y=-1,0
    for i in range(len(stack)-1,-1,-1):
        n,m=stack[i]
        x,y=y,x-(n//m)*y
    return x,y

class MOD:
    def __init__(self,mod):
        self.mod=mod
    
    def Pow(self,a,n):
        a%=self.mod
        if n>=0:
            return pow(a,n,self.mod)
        else:
            assert math.gcd(a,self.mod)==1
            x=Extended_Euclid(a,self.mod)[0]
            return pow(x,-n,self.mod)

    def Build_Fact(self,N):
        assert N>=0
        self.factorial=[1]
        for i in range(1,N+1):
            self.factorial.append((self.factorial[-1]*i)%self.mod)
        self.factorial_inv=[None]*(N+1)
        self.factorial_inv[-1]=self.Pow(self.factorial[-1],-1)
        for i in range(N-1,-1,-1):
            self.factorial_inv[i]=(self.factorial_inv[i+1]*(i+1))%self.mod
        return self.factorial_inv

    def Fact(self,N):
        return self.factorial[N]

    def Fact_Inv(self,N):
        return self.factorial_inv[N]

    def Comb(self,N,K):
        if K<0 or K>N:
            return 0
        s=self.factorial[N]
        s=(s*self.factorial_inv[K])%self.mod
        s=(s*self.factorial_inv[N-K])%self.mod
        return s
class Graph:
    def __init__(self,V,edges=False,graph=False,directed=False,weighted=False):
        self.V=V
        self.directed=directed
        self.weighted=weighted
        if not graph:
            self.edges=edges
            self.graph=[[] for i in range(self.V)]
            if weighted:
                for i,j,d in self.edges:
                    self.graph[i].append((j,d))
                    if not self.directed:
                        self.graph[j].append((i,d))
            else:
                for i,j in self.edges:
                    self.graph[i].append(j)
                    if not self.directed:
                        self.graph[j].append(i)
        else:
            self.graph=graph
            self.edges=[]
            for i in range(self.V):
                if self.weighted:
                    for j,d in self.graph[i]:
                        if self.directed or not self.directed and i<=j:
                            self.edges.append((i,j,d))
                else:
                    for j in self.graph[i]:
                        if self.directed or not self.directed and i<=j:
                            self.edges.append((i,j))

    def SS_BFS(self,s,bipartite_graph=False,linked_components=False,parents=False,unweighted_dist=False,weighted_dist=False):
        seen=[False]*self.V
        seen[s]=True
        if linked_components:
            lc=[s]
        if parents:
            ps=[None]*self.V
            ps[s]=s
        if unweighted_dist or bipartite_graph:
            uwd=[float('inf')]*self.V
            uwd[s]=0
        if weighted_dist:
            wd=[float('inf')]*self.V
            wd[s]=0
        queue=deque([s])
        while queue:
            x=queue.popleft()
            for y in self.graph[x]:
                if self.weighted:
                    y,d=y
                if not seen[y]:
                    seen[y]=True
                    queue.append(y)
                    if linked_components:
                        lc.append(y)
                    if parents:
                        ps[y]=x
                    if unweighted_dist or bipartite_graph:
                        uwd[y]=uwd[x]+1
                    if weighted_dist:
                        wd[y]=wd[x]+d
        if bipartite_graph:
            bg=[[],[]]
            for tpl in self.edges:
                i,j=tpl[:2] if self.weighted else tpl
                if type(uwd[i])==float or type(uwd[j])==float:
                    continue
                if not uwd[i]%2^uwd[j]%2:
                    bg=False
                    break
            else:
                for x in range(self.V):
                    if type(uwd[x])==float:
                        continue
                    bg[uwd[x]%2].append(x)
        tpl=()
        if bipartite_graph:
            tpl+=(bg,)
        if linked_components:
            tpl+=(lc,)
        if parents:
            tpl+=(ps,)
        if unweighted_dist:
            tpl+=(uwd,)
        if weighted_dist:
            tpl+=(wd,)
        if len(tpl)==1:
            tpl=tpl[0]
        return tpl

    def AP_BFS(self,bipartite_graph=False,linked_components=False,parents=False):
        seen=[False]*self.V
        if bipartite_graph:
            bg=[None]*self.V
            cnt=-1
        if linked_components:
            lc=[]
        if parents:
            ps=[None]*self.V
        for s in range(self.V):
            if seen[s]:
                continue
            seen[s]=True
            if bipartite_graph:
                cnt+=1
                bg[s]=(cnt,s&2)
            if linked_components:
                lc.append([s])
            if parents:
                ps[s]=s
            queue=deque([s])
            while queue:
                x=queue.popleft()
                for y in self.graph[x]:
                    if self.weighted:
                        y,d=y
                    if not seen[y]:
                        seen[y]=True
                        queue.append(y)
                        if bipartite_graph:
                            bg[y]=(cnt,bg[x][1]^1)
                        if linked_components:
                            lc[-1].append(y)
                        if parents:
                            ps[y]=x
        if bipartite_graph:
            bg_=bg
            bg=[[[],[]] for i in range(cnt+1)]
            for tpl in self.edges:
                i,j=tpl[:2] if self.weighted else tpl
                if not bg_[i][1]^bg_[j][1]:
                    bg[bg_[i][0]]=False
            for x in range(self.V):
                if bg[bg_[x][0]]:
                    bg[bg_[x][0]][bg_[x][1]].append(x)
        tpl=()
        if bipartite_graph:
            tpl+=(bg,)
        if linked_components:
            tpl+=(lc,)
        if parents:
            tpl+=(ps,)
        if len(tpl)==1:
            tpl=tpl[0]
        return tpl

    def SS_DFS(self,s,bipartite_graph=False,cycle_detection=False,directed_acyclic=False,euler_tour=False,linked_components=False,parents=False,postorder=False,preorder=False,topological_sort=False,unweighted_dist=False,weighted_dist=False):
        seen=[False]*self.V
        finished=[False]*self.V
        if directed_acyclic or cycle_detection or topological_sort:
            dag=True
        if euler_tour:
            et=[]
        if linked_components:
            lc=[]
        if parents or cycle_detection:
            ps=[None]*self.V
            ps[s]=s
        if postorder or topological_sort:
            post=[]
        if preorder:
            pre=[]
        if unweighted_dist or bipartite_graph:
            uwd=[float('inf')]*self.V
            uwd[s]=0
        if weighted_dist:
            wd=[float('inf')]*self.V
            wd[s]=0
        stack=[(s,0)] if self.weighted else [s]
        while stack:
            if self.weighted:
                x,d=stack.pop()
            else:
                x=stack.pop()
            if not seen[x]:
                seen[x]=True
                stack.append((x,d) if self.weighted else x)
                if euler_tour:
                    et.append(x)
                if linked_components:
                    lc.append(x)
                if preorder:
                    pre.append(x)
                for y in self.graph[x]:
                    if self.weighted:
                        y,d=y
                    if not seen[y]:
                        stack.append((y,d) if self.weighted else y)
                        if parents or cycle_detection:
                            ps[y]=x
                        if unweighted_dist or bipartite_graph:
                            uwd[y]=uwd[x]+1
                        if weighted_dist:
                            wd[y]=wd[x]+d
                    elif not finished[y]:
                        if (directed_acyclic or cycle_detection or topological_sort) and dag:
                            dag=False
                            if cycle_detection:
                                cd=(y,x)
            elif not finished[x]:
                finished[x]=True
                if euler_tour:
                    et.append(~x)
                if postorder or topological_sort:
                    post.append(x)
        if bipartite_graph:
            bg=[[],[]]
            for tpl in self.edges:
                i,j=tpl[:2] if self.weighted else tpl
                if type(uwd[i])==float or type(uwd[j])==float:
                    continue
                if not uwd[i]%2^uwd[j]%2:
                    bg=False
                    break
            else:
                for x in range(self.V):
                    if type(uwd[x])==float:
                        continue
                    bg[uwd[x]%2].append(x)
        tpl=()
        if bipartite_graph:
            tpl+=(bg,)
        if cycle_detection:
            if dag:
                cd=[]
            else:
                y,x=cd
                cd=self.Route_Restoration(y,x,ps)
            tpl+=(cd,)
        if directed_acyclic:
            tpl+=(dag,)
        if euler_tour:
            tpl+=(et,)
        if linked_components:
            tpl+=(lc,)
        if parents:
            tpl+=(ps,)
        if postorder:
            tpl+=(post,)
        if preorder:
            tpl+=(pre,)
        if topological_sort:
            if dag:
                tp_sort=post[::-1]
            else:
                tp_sort=[]
            tpl+=(tp_sort,)
        if unweighted_dist:
            tpl+=(uwd,)
        if weighted_dist:
            tpl+=(wd,)
        if len(tpl)==1:
            tpl=tpl[0]
        return tpl

    def AP_DFS(self,bipartite_graph=False,cycle_detection=False,directed_acyclic=False,euler_tour=False,linked_components=False,parents=False,postorder=False,preorder=False,topological_sort=False):
        seen=[False]*self.V
        finished=[False]*self.V
        if bipartite_graph:
            bg=[None]*self.V
            cnt=-1
        if directed_acyclic or cycle_detection or topological_sort:
            dag=True
        if euler_tour:
            et=[]
        if linked_components:
            lc=[]
        if parents or cycle_detection:
            ps=[None]*self.V
        if postorder or topological_sort:
            post=[]
        if preorder:
            pre=[]
        for s in range(self.V):
            if seen[s]:
                continue
            if bipartite_graph:
                cnt+=1
                bg[s]=(cnt,s&2)
            if linked_components:
                lc.append([])
            if parents:
                ps[s]=s
            stack=[(s,0)] if self.weighted else [s]
            while stack:
                if self.weighted:
                    x,d=stack.pop()
                else:
                    x=stack.pop()
                if not seen[x]:
                    seen[x]=True
                    stack.append((x,d) if self.weighted else x)
                    if euler_tour:
                        et.append(x)
                    if linked_components:
                        lc[-1].append(x)
                    if preorder:
                        pre.append(x)
                    for y in self.graph[x]:
                        if self.weighted:
                            y,d=y
                        if not seen[y]:
                            stack.append((y,d) if self.weighted else y)
                            if bipartite_graph:
                                bg[y]=(cnt,bg[x][1]^1)
                            if parents or cycle_detection:
                                ps[y]=x
                        elif not finished[y]:
                            if directed_acyclic and dag:
                                dag=False
                                if cycle_detection:
                                    cd=(y,x)
                elif not finished[x]:
                    finished[x]=True
                    if euler_tour:
                        et.append(~x)
                    if postorder or topological_sort:
                        post.append(x)
        if bipartite_graph:
            bg_=bg
            bg=[[[],[]] for i in range(cnt+1)]
            for tpl in self.edges:
                i,j=tpl[:2] if self.weighted else tpl
                if not bg_[i][1]^bg_[j][1]:
                    bg[bg_[i][0]]=False
            for x in range(self.V):
                if bg[bg_[x][0]]:
                    bg[bg_[x][0]][bg_[x][1]].append(x)
        tpl=()
        if bipartite_graph:
            tpl+=(bg,)
        if cycle_detection:
            if dag:
                cd=[]
            else:
                y,x=cd
                cd=self.Route_Restoration(y,x,ps)
            tpl+=(cd,)
        if directed_acyclic:
            tpl+=(dag,)
        if euler_tour:
            tpl+=(et,)
        if linked_components:
            tpl+=(lc,)
        if parents:
            tpl+=(ps,)
        if postorder:
            tpl+=(post,)
        if preorder:
            tpl+=(pre,)
        if topological_sort:
            if dag:
                tp_sort=post[::-1]
            else:
                tp_sort=[]
            tpl+=(tp_sort,)
        if len(tpl)==1:
            tpl=tpl[0]
        return tpl

    def Tree_Diameter(self,weighted=False):
        def Farthest_Point(u):
            dist=self.SS_BFS(u,weighted_dist=True) if self.weighted else self.SS_BFS(u,unweighted_dist=True)
            fp=0
            for i in range(self.V):
                if dist[fp]<dist[i]:
                    fp=i
            return fp,dist[fp]
        u,d=Farthest_Point(0)
        v,d=Farthest_Point(u)
        return u,v,d

    def SCC(self):
        reverse_graph=[[] for i in range(self.V)]
        for tpl in self.edges:
            i,j=tpl[:2] if self.weighted else tpl
            reverse_graph[j].append(i)
        postorder=self.AP_DFS(postorder=True)
        scc=[]
        seen=[False]*self.V
        for s in postorder[::-1]:
            if seen[s]:
                continue
            queue=deque([s])
            seen[s]=True
            lst=[]
            while queue:
                x=queue.popleft()
                lst.append(x)
                for y in reverse_graph[x]:
                    if self.weighted:
                        y=y[0]
                    if not seen[y]:
                        seen[y]=True
                        queue.append(y)
            scc.append(lst)
        return scc

    def Build_LCA(self,s):
        self.euler_tour,self.parents,depth=self.SS_DFS(s,euler_tour=True,parents=True,unweighted_dist=True)
        self.dfs_in_index=[None]*self.V
        self.dfs_out_index=[None]*self.V
        for i,x in enumerate(self.euler_tour):
            if x>=0:
                self.dfs_in_index[x]=i
            else:
                self.dfs_out_index[~x]=i
        self.ST=Segment_Tree(2*self.V,lambda x,y:min(x,y),float('inf'))
        lst=[None]*2*self.V
        for i in range(2*self.V):
            if self.euler_tour[i]>=0:
                lst[i]=depth[self.euler_tour[i]]
            else:
                lst[i]=depth[self.parents[~self.euler_tour[i]]]
        self.ST.Build(lst)

    def LCA(self,a,b):
        m=min(self.dfs_in_index[a],self.dfs_in_index[b])
        M=max(self.dfs_in_index[a],self.dfs_in_index[b])
        x=self.euler_tour[self.ST.Fold_Index(m,M+1)]
        if x>=0:
            return x
        else:
            return self.parents[~x]

    def Dijkstra(self,s,route_restoration=False):
        dist=[float('inf')]*self.V
        dist[s]=0
        hq=[(0,s)]
        if route_restoration:
            parents=[None]*self.V
            parents[s]=s
        while hq:
            dx,x=heapq.heappop(hq)
            if dist[x]<dx:
                continue
            for y,dy in self.graph[x]:
                if dist[y]>dx+dy:
                    dist[y]=dx+dy
                    if route_restoration:
                        parents[y]=x
                    heapq.heappush(hq,(dist[y],y))
        if route_restoration:
            return dist,parents
        else:
            return dist

    def Bellman_Ford(self,s,route_restoration=False):
        dist=[float('inf')]*self.V
        dist[s]=0
        if route_restoration:
            parents=[s]*self.V
        for _ in range(self.V-1):
            for i,j,d in self.edges:
                if dist[j]>dist[i]+d:
                    dist[j]=dist[i]+d
                    if route_restoration:
                        parents[j]=i
                if not self.directed and dist[i]>dist[j]+d:
                    dist[i]=dist[j]+d
                    if route_restoration:
                        parents[i]=j
        negative_cycle=[]
        for i,j,d in self.edges:
            if dist[j]>dist[i]+d:
                negative_cycle.append(j)
            if not self.directed and dist[i]>dist[j]+d:
                negative_cycle.append(i)
        if negative_cycle:
            is_negative_cycle=[False]*self.V
            for i in negative_cycle:
                if is_negative_cycle[i]:
                    continue
                else:
                    queue=deque([i])
                    is_negative_cycle[i]=True
                    while queue:
                        x=queue.popleft()
                        for y,d in self.graph[x]:
                            if not is_negative_cycle[y]:
                                queue.append(y)
                                is_negative_cycle[y]=True
                                if route_restoration:
                                    parents[y]=x
            for i in range(self.V):
                if is_negative_cycle[i]:
                    dist[i]=-float('inf')
        if route_restoration:
            return dist,parents
        else:
            return dist

    def Warshall_Floyd(self,route_restoration=False):
        dist=[[float('inf')]*self.V for i in range(self.V)]
        for i in range(self.V):
            dist[i][i]=0
        if route_restoration:
            parents=[[j for j in range(self.V)] for i in range(self.V)]
        for i,j,d in self.edges:
            if dist[i][j]>d:
                dist[i][j]=d
                if route_restoration:
                    parents[i][j]=i
            if not self.directed and dist[j][i]>d:
                dist[j][i]=d
                if route_restoration:
                    parents[j][i]=j
        for k in range(self.V):
            for i in range(self.V):
                for j in range(self.V):
                    if dist[i][j]>dist[i][k]+dist[k][j]:
                        dist[i][j]=dist[i][k]+dist[k][j]
                        if route_restoration:
                            parents[i][j]=parents[k][j]
        for i in range(self.V):
            if dist[i][i]<0:
                for j in range(self.V):
                    if dist[i][j]!=float('inf'):
                        dist[i][j]=-float('inf')
        if route_restoration:
            return dist,parents
        else:
            return dist

    def Route_Restoration(self,s,g,parents):
        route=[g]
        while s!=g and parents[g]!=g:
            g=parents[g]
            route.append(g)
        route=route[::-1]
        return route

    def Kruskal(self):
        UF=UnionFind(self.V)
        sorted_edges=sorted(self.edges,key=lambda x:x[2])
        minimum_spnning_tree=[]
        for i,j,d in sorted_edges:
            if not UF.Same(i,j):
                UF.Union(i,j)
                minimum_spnning_tree.append((i,j,d))
        return minimum_spnning_tree

    def Ford_Fulkerson(self,s,t):
        max_flow=0
        residual_graph=[defaultdict(int) for i in range(self.V)]
        if self.weighted:
            for i,j,d in self.edges:
                if not d:
                    continue
                residual_graph[i][j]+=d
                if not self.directed:
                    residual_graph[j][i]+=d
        else:
            for i,j in self.edges:
                residual_graph[i][j]+=1
                if not self.directed:
                    residual_graph[j][i]+=1
        while True:
            parents=[None]*self.V
            parents[s]=s
            seen=[False]*self.V
            seen[s]=True
            queue=deque([s])
            while queue:
                x=queue.popleft()
                for y in residual_graph[x].keys():
                    if not seen[y]:
                        seen[y]=True
                        queue.append(y)
                        parents[y]=x
                        if y==t:
                            tt=t
                            while tt!=s:
                                residual_graph[parents[tt]][tt]-=1
                                residual_graph[tt][parents[tt]]+=1
                                if not residual_graph[parents[tt]][tt]:
                                    residual_graph[parents[tt]].pop(tt)
                                tt=parents[tt]
                            max_flow+=1
                            break
                else:
                    continue
                break
            else:
                break
        return max_flow

    def BFS(self,s):
        seen=[False]*self.V
        seen[s]=True
        queue=deque([s])

        while queue:
            x=queue.popleft()
            for y in self.graph[x]:
                if self.weighted:
                    y,d=y
                if not seen[y]:
                    seen[y]=True
                    queue.append(y)
                    
        return 

    def DFS(self,s):
        seen=[False]*self.V
        finished=[False]*self.V
        stack=[(s,0)] if self.weighted else [s]

        while stack:
            if self.weighted:
                x,d=stack.pop()
            else:
                x=stack.pop()
            if not seen[x]:
                seen[x]=True
                stack.append((x,d) if self.weighted else x)

                for y in self.graph[x]:
                    if self.weighted:
                        y,d=y
                    if not seen[y]:
                        stack.append((y,d) if self.weighted else y)
            elif not finished[x]:
                finished[x]=True
                
        return 

class Segment_Tree:
    def __init__(self,N,f,e,lst=None):
        self.f=f
        self.e=e
        self.N=N
        if lst==None:
            self.segment_tree=[self.e]*2*self.N
        else:
            assert len(lst)<=self.N
            self.segment_tree=[self.e]*self.N+[x for x in lst]+[self.e]*(N-len(lst))
            for i in range(self.N-1,0,-1):
                self.segment_tree[i]=self.f(self.segment_tree[i<<1],self.segment_tree[i<<1|1])

    def __getitem__(self,i):
        if type(i)==int:
            if -self.N<=i<0:
                return self.segment_tree[i+self.N*2]
            elif 0<=i<self.N:
                return self.segment_tree[i+self.N]
            else:
                raise IndexError('list index out of range')
        else:
            a,b,c=i.start,i.stop,i.step
            if a==None or a<-self.N:
                a=self.N
            elif self.N<=a:
                a=self.N*2
            elif a<0:
                a+=self.N*2
            else:
                a+=self.N
            if b==None or self.N<=b:
                b=self.N*2
            elif b<-self.N:
                b=self.N
            elif b<0:
                b+=self.N*2
            else:
                b+=self.N
            return self.segment_tree[slice(a,b,c)]
    
    def __setitem__(self,i,x):
        if -self.N<=i<0:
            i+=self.N*2
        elif 0<=i<self.N:
            i+=self.N
        else:
            raise IndexError('list index out of range')
        self.segment_tree[i]=x
        while i>1:
            i>>= 1
            self.segment_tree[i]=self.f(self.segment_tree[i<<1],self.segment_tree[i<<1|1])
    
    def Build(self,lst):
        for i,x in enumerate(lst,self.N):
            self.segment_tree[i]=x
        for i in range(self.N-1,0,-1):
            self.segment_tree[i]=self.f(self.segment_tree[i<<1],self.segment_tree[i<<1|1])

    def Fold(self,L=None,R=None):
        if L==None or L<-self.N:
            L=self.N
        elif self.N<=L:
            L=self.N*2
        elif L<0:
            L+=self.N*2
        else:
            L+=self.N
        if R==None or self.N<=R:
            R=self.N*2
        elif R<-self.N:
            R=self.N
        elif R<0:
            R+=self.N*2
        else:
            R+=self.N
        vL=self.e
        vR=self.e
        while L<R:
            if L&1:
                vL=self.f(vL,self.segment_tree[L])
                L+=1
            if R&1:
                R-=1
                vR=self.f(self.segment_tree[R],vR)
            L>>=1
            R>>=1
        return self.f(vL,vR)

    def Fold_Index(self,L=None,R=None):
        if L==None or L<-self.N:
            L=self.N
        elif self.N<=L:
            L=self.N*2
        elif L<0:
            L+=self.N*2
        else:
            L+=self.N
        if R==None or self.N<=R:
            R=self.N*2
        elif R<-self.N:
            R=self.N
        elif R<0:
            R+=self.N*2
        else:
            R+=self.N
        if L==R:
            return None
        x=self.Fold(L-self.N,R-self.N)
        while L<R:
            if L&1:
                if self.segment_tree[L]==x:
                    i=L
                    break
                L+=1
            if R&1:
                R-=1
                if self.segment_tree[R]==x:
                    i=R
                    break
            L>>=1
            R>>=1
        while i<self.N:
            if self.segment_tree[i]==self.segment_tree[i<<1]:
                i<<=1
            else:
                i<<=1
                i|=1
        i-=self.N
        return i

    def __str__(self):
        return '['+', '.join(map(str,self.segment_tree[self.N:]))+']'

N=int(readline())
mod=10**9+7
edges=[]
ans=0
for _ in range(N-1):
    x,y=map(int,readline().split())
    x-=1;y-=1
    edges.append((x,y))
G=Graph(N,edges=edges)
MD=MOD(mod=mod)
MD.Build_Fact(1000)

pow_lst=[1]
for _ in range(1000):
    pow_lst.append(pow_lst[-1]*500000004%mod)

@lru_cache(maxsize=None)
def f(a,b):
    if a:
        return (f(a-1,b)+pow_lst[b+a-1]*MD.Comb(b-2+a,a-1))%mod
    return 0
for z in range(N):
    parents,postorder,depth=G.SS_DFS(z,parents=True,postorder=True,unweighted_dist=True)
    children=[[r] for r in range(N)]
    for r in postorder:
        for x in G.graph[r]:
            if x==parents[r]:
                continue
            for y in children[x]:
                children[r].append(y)
        for x in children[r]:
            if r>x:
                ans+=1
        for x in G.graph[r]:
            if x==parents[r]:
                continue
            for y in G.graph[r]:
                if y==parents[r]:
                    continue
                if x!=y:
                    for xx in children[x]:
                        for yy in children[y]:
                            if xx<yy:
                                a,b=depth[xx]-depth[r],depth[yy]-depth[r]
                                ans+=f(a,b)
                                ans%=mod
ans*=MD.Pow(N,-1)
ans%=mod
print(ans)