結果

問題 No.329 全射
ユーザー vwxyzvwxyz
提出日時 2021-09-03 19:12:35
言語 PyPy3
(7.3.15)
結果
AC  
実行時間 361 ms / 2,000 ms
コード長 25,002 bytes
コンパイル時間 440 ms
コンパイル使用メモリ 82,304 KB
実行使用メモリ 107,520 KB
最終ジャッジ日時 2024-05-08 22:30:35
合計ジャッジ時間 11,950 ms
ジャッジサーバーID
(参考情報)
judge5 / judge4
このコードへのチャレンジ
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テストケース

テストケース表示
入力 結果 実行時間
実行使用メモリ
testcase_00 AC 166 ms
89,344 KB
testcase_01 AC 168 ms
89,600 KB
testcase_02 AC 169 ms
89,600 KB
testcase_03 AC 169 ms
89,472 KB
testcase_04 AC 169 ms
89,600 KB
testcase_05 AC 163 ms
89,472 KB
testcase_06 AC 163 ms
89,600 KB
testcase_07 AC 170 ms
89,472 KB
testcase_08 AC 167 ms
89,600 KB
testcase_09 AC 169 ms
89,344 KB
testcase_10 AC 166 ms
89,472 KB
testcase_11 AC 163 ms
89,472 KB
testcase_12 AC 170 ms
89,472 KB
testcase_13 AC 336 ms
104,144 KB
testcase_14 AC 236 ms
99,200 KB
testcase_15 AC 264 ms
99,720 KB
testcase_16 AC 315 ms
104,960 KB
testcase_17 AC 296 ms
100,984 KB
testcase_18 AC 361 ms
107,520 KB
testcase_19 AC 344 ms
105,272 KB
testcase_20 AC 346 ms
104,832 KB
testcase_21 AC 301 ms
103,372 KB
testcase_22 AC 291 ms
100,264 KB
testcase_23 AC 239 ms
99,328 KB
testcase_24 AC 235 ms
99,728 KB
testcase_25 AC 269 ms
100,724 KB
testcase_26 AC 240 ms
98,944 KB
testcase_27 AC 210 ms
98,432 KB
testcase_28 AC 187 ms
89,600 KB
testcase_29 AC 202 ms
98,048 KB
testcase_30 AC 194 ms
98,048 KB
testcase_31 AC 163 ms
89,600 KB
testcase_32 AC 209 ms
98,176 KB
testcase_33 AC 192 ms
98,176 KB
testcase_34 AC 186 ms
98,048 KB
testcase_35 AC 192 ms
97,920 KB
testcase_36 AC 196 ms
97,792 KB
testcase_37 AC 191 ms
97,792 KB
testcase_38 AC 192 ms
98,048 KB
testcase_39 AC 198 ms
97,792 KB
testcase_40 AC 197 ms
97,664 KB
testcase_41 AC 198 ms
98,048 KB
testcase_42 AC 197 ms
97,792 KB
権限があれば一括ダウンロードができます

ソースコード

diff #

import bisect
import copy
import decimal
import fractions
import functools
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

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,subtree_size=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 or subtree_size:
            ps=[None]*self.V
            ps[s]=s
        if postorder or topological_sort:
            post=[]
        if preorder:
            pre=[]
        if subtree_size:
            ss=[1]*self.V
        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 or subtree_size:
                            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 subtree_size:
                    for y in self.graph[x]:
                        if y==ps[x]:
                            continue
                        ss[x]+=ss[y]
        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 subtree_size:
            tpl+=(ss,)
        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 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 

def Stirling_Second_Numbers(N,K,mod=0):
    stirling_second_numbers=[[0]*(K+1) for i in range(N+1)]
    for n in range(1,N+1):
        stirling_second_numbers[n][1]=1
        for k in range(2,n+1):
            stirling_second_numbers[n][k]=stirling_second_numbers[n-1][k-1]+k*stirling_second_numbers[n-1][k]
            if mod:
                stirling_second_numbers[n][k]%=mod
    return stirling_second_numbers

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,p,e=1):
        self.p=p
        self.e=e
        self.mod=self.p**self.e

    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]
        self.cnt=[0]*(N+1)
        for i in range(1,N+1):
            ii=i
            self.cnt[i]=self.cnt[i-1]
            while ii%self.p==0:
                ii//=self.p
                self.cnt[i]+=1
            self.factorial.append((self.factorial[-1]*ii)%self.mod)
        self.factorial_inve=[None]*(N+1)
        self.factorial_inve[-1]=self.Pow(self.factorial[-1],-1)
        for i in range(N-1,-1,-1):
            ii=i+1
            while ii%self.p==0:
                ii//=self.p
            self.factorial_inve[i]=(self.factorial_inve[i+1]*ii)%self.mod

    def Fact(self,N):
        return self.factorial[N]*pow(self.p,self.cnt[N],self.mod)%self.mod

    def Fact_Inve(self,N):
        if self.cnt[N]:
            return None
        return self.factorial_inve[N]

    def Comb(self,N,K,divisible_count=False):
        if K<0 or K>N:
            return 0
        retu=self.factorial[N]*self.factorial_inve[K]*self.factorial_inve[N-K]%self.mod
        cnt=self.cnt[N]-self.cnt[N-K]-self.cnt[K]
        if divisible_count:
            return retu,cnt
        else:
            retu*=pow(self.p,cnt,self.mod)
            retu%=self.mod
            return retu

N,M=map(int,readline().split())
W=list(map(int,readline().split()))
mod=10**9+7
MD=MOD(mod)
MD.Build_Fact(10**3)
SSN=Stirling_Second_Numbers(1000,1000,mod=mod)
edges=[]
for _ in range(M):
    i,j=map(int,readline().split())
    i-=1;j-=1
    edges.append((j,i))
ans=0
for s in range(N):
    edges_=[]
    for j,i in edges:
        if W[i]>=W[s] and W[j]>=W[s]:
            edges_.append((j,i))
    G=Graph(N,edges=edges_,directed=True)
    dist=G.SS_BFS(s,unweighted_dist=True)
    for t in range(N):
        if dist[t]!=float('inf'):
            ans+=SSN[W[t]][W[s]]*MD.Fact(W[s])
            ans%=mod
print(ans)
0