#pragma GCC optimize ("Ofast") #include using namespace std; void*wmem; char memarr[96000000]; template inline void walloc1d(T **arr, int x, void **mem = &wmem){ static int skip[16] = {0, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1}; (*mem) = (void*)( ((char*)(*mem)) + skip[((unsigned long long)(*mem)) & 15] ); (*arr)=(T*)(*mem); (*mem)=((*arr)+x); } template inline void walloc1d(T **arr, int x1, int x2, void **mem = &wmem){ walloc1d(arr, x2-x1, mem); (*arr) -= x1; } inline int my_getchar_unlocked(){ static char buf[1048576]; static int s = 1048576; static int e = 1048576; if(s == e && e == 1048576){ e = fread_unlocked(buf, 1, 1048576, stdin); s = 0; } if(s == e){ return EOF; } return buf[s++]; } inline void rd(int &x){ int k; int m=0; x=0; for(;;){ k = my_getchar_unlocked(); if(k=='-'){ m=1; break; } if('0'<=k&&k<='9'){ x=k-'0'; break; } } for(;;){ k = my_getchar_unlocked(); if(k<'0'||k>'9'){ break; } x=x*10+k-'0'; } if(m){ x=-x; } } struct MY_WRITER{ char buf[1048576]; int s; int e; MY_WRITER(){ s = 0; e = 1048576; } ~MY_WRITER(){ if(s){ fwrite_unlocked(buf, 1, s, stdout); } } } ; MY_WRITER MY_WRITER_VAR; void my_putchar_unlocked(int a){ if(MY_WRITER_VAR.s == MY_WRITER_VAR.e){ fwrite_unlocked(MY_WRITER_VAR.buf, 1, MY_WRITER_VAR.s, stdout); MY_WRITER_VAR.s = 0; } MY_WRITER_VAR.buf[MY_WRITER_VAR.s++] = a; } inline void wt_L(char a){ my_putchar_unlocked(a); } inline void wt_L(const char c[]){ int i=0; for(i=0;c[i]!='\0';i++){ my_putchar_unlocked(c[i]); } } template int arrCountVal(int N, T A[], S val){ int i; int res = 0; for(i=(0);i<(N);i++){ if(A[i]==val){ res++; } } return res; } struct graph{ int N; int*es; int**edge; void setEdge(int N__, int M, int A[], int B[], void **mem = &wmem){ int i; N = N__; walloc1d(&es, N, mem); walloc1d(&edge, N, mem); for(i=(0);i<(N);i++){ es[i] = 0; } for(i=(0);i<(M);i++){ es[A[i]]++; es[B[i]]++; } for(i=(0);i<(N);i++){ walloc1d(&edge[i], es[i], mem); } for(i=(0);i<(N);i++){ es[i] = 0; } for(i=(0);i<(M);i++){ edge[A[i]][es[A[i]]++] = B[i]; edge[B[i]][es[B[i]]++] = A[i]; } } void getDist(int root, int res[], void *mem = wmem){ int i; int j; int k; int*q; int s; int z; walloc1d(&q, N, &mem); for(i=(0);i<(N);i++){ res[i]=-1; } res[root]=0; s=0; z=1; q[0]=root; while(z){ i=q[s++]; z--; for(j=(0);j<(es[i]);j++){ k=edge[i][j]; if(res[k]>=0){ continue; } res[k]=res[i]+1; q[s+z++]=k; } } } int getDist(int a, int b, void *mem = wmem){ int i; int j; int k; int*q; int s; int z; int*d; if(a==b){ return 0; } walloc1d(&d, N, &mem); walloc1d(&q, N, &mem); for(i=(0);i<(N);i++){ d[i] = -1; } d[a] = 0; s = 0; z = 1; q[0] = a; while(z){ i = q[s++]; z--; for(j=(0);j<(es[i]);j++){ k = edge[i][j]; if(d[k] >= 0){ continue; } d[k] = d[i] + 1; if(k==b){ return d[k]; } q[s+z++] = k; } } return -1; } int TreeDiameter(int &a, int &b, void *mem = wmem){ int i; int mx; int*d; walloc1d(&d, N, &mem); getDist(0, d, mem); mx = -1; for(i=(0);i<(N);i++){ if(mx < d[i]){ mx = d[i]; a = i; } } getDist(a, d, mem); mx = -1; for(i=(0);i<(N);i++){ if(mx < d[i]){ mx = d[i]; b = i; } } return mx; } int TreeDiameter(void *mem = wmem){ int a; int b; return TreeDiameter(a, b, mem); } } ; int N; int A[100000]; int B[100000]; graph g; int d1[100000]; int d2[100000]; int d[100000]; int main(){ int i; wmem = memarr; int x; int y; int m; int mx = -1; rd(N); { int Lj4PdHRW; for(Lj4PdHRW=(0);Lj4PdHRW<(N-1);Lj4PdHRW++){ rd(A[Lj4PdHRW]);A[Lj4PdHRW] += (-1); rd(B[Lj4PdHRW]);B[Lj4PdHRW] += (-1); } } g.setEdge(N,N-1,A,B); if(arrCountVal(N,g.es,1) == 2){ wt_L("Yes"); wt_L('\n'); return 0; } m = g.TreeDiameter(x, y); g.getDist(x, d1); g.getDist(y, d2); for(i=(0);i<(N);i++){ if(d1[i]==d2[i] && mx < d1[i]+d2[i]){ mx = d1[i]+d2[i]; m = i; } } if(mx == -1){ wt_L("No"); wt_L('\n'); return 0; } g.getDist(m, d); mx = -1; for(i=(0);i<(N);i++){ if(g.es[i]==1 && i!=m){ if(mx == -1){ mx = d[i]; } if(mx != d[i]){ wt_L("No"); wt_L('\n'); return 0; } } } wt_L("Yes"); wt_L('\n'); return 0; } // cLay version 20210227-1 // --- original code --- // int N, A[1d5], B[1d5]; // graph g; // int d1[1d5], d2[1d5], d[1d5]; // { // int x, y, m, mx = -1; // rd(N,(A--,B--)(N-1)); // g.setEdge(N,N-1,A,B); // if(arrCountVal(N,g.es,1) == 2) wt("Yes"), return 0; // m = g.TreeDiameter(x, y); // g.getDist(x, d1); // g.getDist(y, d2); // rep(i,N) if(d1[i]==d2[i] && mx < d1[i]+d2[i]) mx = d1[i]+d2[i], m = i; // if(mx == -1) wt("No"), return 0; // g.getDist(m, d); // mx = -1; // rep(i,N) if(g.es[i]==1 && i!=m){ // if(mx == -1) mx = d[i]; // if(mx != d[i]) wt("No"), return 0; // } // wt("Yes"); // }