// File: Laakeri[P]Triangulator/src/hyper.cpp
// Function: Hyper::solveFrac()
void solveFrac() {
	Timer timer;
	timer.start();
	HyperIO io;
	vector<vector<int> > hEdges = io.readInput(cin);
	set<pair<int, int> > pEdges;
	for (auto& he : hEdges) {
		for (int i = 0; i < (int)he.size(); i++) {
			for (int ii = i+1; ii < (int)he.size(); ii++) {
				pEdges.insert({he[i], he[ii]});
			}
		}
	}
	Graph pGraph(pEdges);
	vector<vector<int> > hes = hEdges;
	for (auto& he : hes) {
		for (int& x : he) {
			x = pGraph.mapInto(x);
		}
		sort(he.begin(), he.end());
	}
	SetCover::init(hes);
	vector<int> vert(pGraph.n);
	for (int i = 0; i < pGraph.n; i++) {
		vert[i] = i;
	}
	auto sol = SolveGraph::solveFracGraph(pGraph, 0, 0, (ld)hes.size(), vert);
	sol.S = pGraph.mapBack(sol.S);
	io.printFill(cout, sol.S);
	cerr<<setprecision(8)<<"Fractional hypertreewidth: "<<sol.F<<endl;
	cerr<<"*Fill edges: "<<sol.S.size()<<endl;
	cerr<<"Time "<<timer.getTime().count()<<endl;
}

// Assembly:
pushq %rbp
movq %rsp, %rbp
subq $0x330, %rsp            # imm = 0x330
leaq -0x18(%rbp), %rdi
movq %rdi, -0x260(%rbp)
callq 0x55820
movq -0x260(%rbp), %rdi
callq 0x55870
leaq -0x30(%rbp), %rdi
movq %rdi, -0x258(%rbp)
callq 0x24190
movq -0x258(%rbp), %rsi
movq 0x58f53(%rip), %rdx     # 0x79fd8
leaq -0x48(%rbp), %rdi
callq 0x241b0
jmp 0x21090
leaq -0x88(%rbp), %rdi
callq 0x55b0
leaq -0x48(%rbp), %rax
movq %rax, -0x90(%rbp)
movq -0x90(%rbp), %rdi
callq 0x58e0
movq %rax, -0x98(%rbp)
movq -0x90(%rbp), %rdi
callq 0x5910
movq %rax, -0xa0(%rbp)
leaq -0x98(%rbp), %rdi
leaq -0xa0(%rbp), %rsi
callq 0x5940
testb $0x1, %al
jne 0x210e9
jmp 0x21247
leaq -0x98(%rbp), %rdi
callq 0x5980
movq %rax, -0xa8(%rbp)
movl $0x0, -0xac(%rbp)
movl -0xac(%rbp), %eax
movl %eax, -0x264(%rbp)
movq -0xa8(%rbp), %rdi
callq 0x59a0
movq %rax, %rcx
movl -0x264(%rbp), %eax
cmpl %ecx, %eax
jge 0x21234
movl -0xac(%rbp), %eax
addl $0x1, %eax
movl %eax, -0xb0(%rbp)
movl -0xb0(%rbp), %eax
movl %eax, -0x268(%rbp)
movq -0xa8(%rbp), %rdi
callq 0x59a0
movq %rax, %rcx
movl -0x268(%rbp), %eax
cmpl %ecx, %eax
jge 0x2121e
movq -0xa8(%rbp), %rdi
movslq -0xac(%rbp), %rsi
callq 0x178f0
movq %rax, -0x270(%rbp)
movq -0xa8(%rbp), %rdi
movslq -0xb0(%rbp), %rsi
callq 0x178f0
movq -0x270(%rbp), %rsi
movq %rax, %rdx
leaq -0xb8(%rbp), %rdi
callq 0xdfc0
jmp 0x211ac
leaq -0x88(%rbp), %rdi
leaq -0xb8(%rbp), %rsi
callq 0xde40
movb %dl, -0x279(%rbp)
movq %rax, -0x278(%rbp)
jmp 0x211ce
movb -0x279(%rbp), %al
movq -0x278(%rbp), %rcx
movq %rcx, -0xc8(%rbp)
movb %al, -0xc0(%rbp)
movl -0xb0(%rbp), %eax
addl $0x1, %eax
movl %eax, -0xb0(%rbp)
jmp 0x2113e
movq %rax, %rcx
movl %edx, %eax
movq %rcx, -0x50(%rbp)
movl %eax, -0x54(%rbp)
jmp 0x2182c
movq %rax, %rcx
movl %edx, %eax
movq %rcx, -0x50(%rbp)
movl %eax, -0x54(%rbp)
jmp 0x21817
jmp 0x21220
movl -0xac(%rbp), %eax
addl $0x1, %eax
movl %eax, -0xac(%rbp)
jmp 0x21106
jmp 0x21236
leaq -0x98(%rbp), %rdi
callq 0x59c0
jmp 0x210cd
leaq -0x120(%rbp), %rdi
leaq -0x88(%rbp), %rsi
callq 0x15430
jmp 0x2125c
leaq -0x138(%rbp), %rdi
leaq -0x48(%rbp), %rsi
callq 0x5d30
jmp 0x2126e
leaq -0x138(%rbp), %rax
movq %rax, -0x140(%rbp)
movq -0x140(%rbp), %rdi
callq 0x58e0
movq %rax, -0x148(%rbp)
movq -0x140(%rbp), %rdi
callq 0x5910
movq %rax, -0x150(%rbp)
leaq -0x148(%rbp), %rdi
leaq -0x150(%rbp), %rsi
callq 0x5940
testb $0x1, %al
jne 0x212be
jmp 0x213db
leaq -0x148(%rbp), %rdi
callq 0x5980
movq %rax, -0x158(%rbp)
movq -0x158(%rbp), %rax
movq %rax, -0x160(%rbp)
movq -0x160(%rbp), %rdi
callq 0xe060
movq %rax, -0x168(%rbp)
movq -0x160(%rbp), %rdi
callq 0xe090
movq %rax, -0x170(%rbp)
leaq -0x168(%rbp), %rdi
leaq -0x170(%rbp), %rsi
callq 0xe0c0
testb $0x1, %al
jne 0x2131e
jmp 0x2138d
leaq -0x168(%rbp), %rdi
callq 0xe100
movq %rax, -0x178(%rbp)
movq -0x178(%rbp), %rax
movl (%rax), %esi
leaq -0x120(%rbp), %rdi
callq 0x17030
movl %eax, -0x280(%rbp)
jmp 0x2134e
movl -0x280(%rbp), %ecx
movq -0x178(%rbp), %rax
movl %ecx, (%rax)
leaq -0x168(%rbp), %rdi
callq 0xe120
jmp 0x21305
movq %rax, %rcx
movl %edx, %eax
movq %rcx, -0x50(%rbp)
movl %eax, -0x54(%rbp)
jmp 0x2180b
movq %rax, %rcx
movl %edx, %eax
movq %rcx, -0x50(%rbp)
movl %eax, -0x54(%rbp)
jmp 0x217ff
movq -0x158(%rbp), %rdi
callq 0xe060
movq %rax, -0x180(%rbp)
movq -0x158(%rbp), %rdi
callq 0xe090
movq %rax, -0x188(%rbp)
movq -0x180(%rbp), %rdi
movq -0x188(%rbp), %rsi
callq 0x176e0
jmp 0x213c8
jmp 0x213ca
leaq -0x148(%rbp), %rdi
callq 0x59c0
jmp 0x212a2
leaq -0x1a0(%rbp), %rdi
leaq -0x138(%rbp), %rsi
callq 0x5d30
jmp 0x213f0
leaq -0x1a0(%rbp), %rdi
callq 0x4b3b0
jmp 0x213fe
leaq -0x1a0(%rbp), %rdi
callq 0x5e20
movslq -0xd0(%rbp), %rax
movq %rax, -0x290(%rbp)
leaq -0x1b9(%rbp), %rdi
movq %rdi, -0x288(%rbp)
callq 0x111b0
movq -0x290(%rbp), %rsi
movq -0x288(%rbp), %rdx
leaq -0x1b8(%rbp), %rdi
callq 0x17ab0
jmp 0x21447
leaq -0x1b9(%rbp), %rdi
callq 0x6620
movl $0x0, -0x1c0(%rbp)
movl -0x1c0(%rbp), %eax
cmpl -0xd0(%rbp), %eax
jge 0x214dd
movl -0x1c0(%rbp), %eax
movl %eax, -0x294(%rbp)
movslq -0x1c0(%rbp), %rsi
leaq -0x1b8(%rbp), %rdi
callq 0x178f0
movl -0x294(%rbp), %ecx
movl %ecx, (%rax)
movl -0x1c0(%rbp), %eax
addl $0x1, %eax
movl %eax, -0x1c0(%rbp)
jmp 0x2145d
movq %rax, %rcx
movl %edx, %eax
movq %rcx, -0x50(%rbp)
movl %eax, -0x54(%rbp)
leaq -0x1a0(%rbp), %rdi
callq 0x5e20
jmp 0x217ff
movq %rax, %rcx
movl %edx, %eax
movq %rcx, -0x50(%rbp)
movl %eax, -0x54(%rbp)
leaq -0x1b9(%rbp), %rdi
callq 0x6620
jmp 0x217ff
leaq -0x138(%rbp), %rdi
callq 0x5e80
movq %rax, -0x250(%rbp)
testq %rax, %rax
sets %al
movzbl %al, %eax
movl %eax, %ecx
fildll -0x250(%rbp)
leaq 0x382a0(%rip), %rax     # 0x597a8
flds (%rax,%rcx,4)
faddp %st, %st(1)
movq %rsp, %rax
fldz
fld %st(0)
fstpt 0x10(%rax)
fstpt (%rax)
fstpt 0x20(%rax)
leaq -0x1f0(%rbp), %rdi
leaq -0x120(%rbp), %rsi
leaq -0x1b8(%rbp), %rdx
callq 0x1ffc0
jmp 0x21538
leaq -0x1e0(%rbp), %rsi
leaq -0x220(%rbp), %rdi
callq 0x56a0
jmp 0x2154d
leaq -0x208(%rbp), %rdi
leaq -0x120(%rbp), %rsi
leaq -0x220(%rbp), %rdx
callq 0x16aa0
jmp 0x21569
leaq -0x1e0(%rbp), %rdi
movq %rdi, -0x2a0(%rbp)
leaq -0x208(%rbp), %rsi
movq %rsi, -0x2a8(%rbp)
callq 0x5790
movq -0x2a8(%rbp), %rdi
callq 0x5470
leaq -0x220(%rbp), %rdi
callq 0x5470
movq -0x2a0(%rbp), %rsi
leaq -0x238(%rbp), %rdi
callq 0x56a0
jmp 0x215b7
movq 0x58a0a(%rip), %rsi     # 0x79fc8
leaq -0x30(%rbp), %rdi
leaq -0x238(%rbp), %rdx
callq 0x24650
jmp 0x215d0
leaq -0x238(%rbp), %rdi
callq 0x5470
movl $0x8, %edi
callq 0x247c0
movl %eax, -0x2ac(%rbp)
jmp 0x215ee
movl -0x2ac(%rbp), %eax
movl %eax, -0x23c(%rbp)
movl -0x23c(%rbp), %esi
movq 0x589e9(%rip), %rdi     # 0x79ff0
callq 0x3430
movq %rax, -0x2b8(%rbp)
jmp 0x21615
movq -0x2b8(%rbp), %rdi
leaq 0x38427(%rip), %rsi     # 0x59a4a
callq 0x32b0
movq %rax, -0x2c0(%rbp)
jmp 0x21631
movq -0x2c0(%rbp), %rdi
fldt -0x1f0(%rbp)
movq %rsp, %rax
fstpt (%rax)
callq 0x3370
movq %rax, -0x2c8(%rbp)
jmp 0x21651
movq -0x2c8(%rbp), %rdi
movq 0x58959(%rip), %rsi     # 0x79fb8
callq 0x3300
jmp 0x21666
movq 0x58983(%rip), %rdi     # 0x79ff0
leaq 0x37b87(%rip), %rsi     # 0x591fb
callq 0x32b0
movq %rax, -0x2d0(%rbp)
jmp 0x21682
leaq -0x1e0(%rbp), %rdi
callq 0x5680
movq -0x2d0(%rbp), %rdi
movq %rax, %rsi
callq 0x3080
movq %rax, -0x2d8(%rbp)
jmp 0x216a6
movq -0x2d8(%rbp), %rdi
movq 0x58904(%rip), %rsi     # 0x79fb8
callq 0x3300
jmp 0x216bb
movq 0x5892e(%rip), %rdi     # 0x79ff0
leaq 0x37e00(%rip), %rsi     # 0x594c9
callq 0x32b0
movq %rax, -0x2e0(%rbp)
jmp 0x216d7
leaq -0x18(%rbp), %rdi
callq 0x55920
movsd %xmm0, -0x2e8(%rbp)
jmp 0x216ea
movsd -0x2e8(%rbp), %xmm0
movsd %xmm0, -0x248(%rbp)
leaq -0x248(%rbp), %rdi
callq 0x57c0
movsd %xmm0, -0x2f0(%rbp)
jmp 0x21710
movsd -0x2f0(%rbp), %xmm0
movq -0x2e0(%rbp), %rdi
callq 0x34c0
movq %rax, -0x2f8(%rbp)
jmp 0x2172d
movq -0x2f8(%rbp), %rdi
movq 0x5887d(%rip), %rsi     # 0x79fb8
callq 0x3300
jmp 0x21742
leaq -0x1f0(%rbp), %rdi
callq 0x24130
leaq -0x1b8(%rbp), %rdi
callq 0x6d30
leaq -0x138(%rbp), %rdi
callq 0x5e20
leaq -0x120(%rbp), %rdi
callq 0x59e0
leaq -0x88(%rbp), %rdi
callq 0x5a70
leaq -0x48(%rbp), %rdi
callq 0x5e20
leaq -0x30(%rbp), %rdi
callq 0x247a0
addq $0x330, %rsp            # imm = 0x330
popq %rbp
retq
movq %rax, %rcx
movl %edx, %eax
movq %rcx, -0x50(%rbp)
movl %eax, -0x54(%rbp)
jmp 0x217f3
movq %rax, %rcx
movl %edx, %eax
movq %rcx, -0x50(%rbp)
movl %eax, -0x54(%rbp)
jmp 0x217e7
movq %rax, %rcx
movl %edx, %eax
movq %rcx, -0x50(%rbp)
movl %eax, -0x54(%rbp)
leaq -0x220(%rbp), %rdi
callq 0x5470
jmp 0x217e7
movq %rax, %rcx
movl %edx, %eax
movq %rcx, -0x50(%rbp)
movl %eax, -0x54(%rbp)
leaq -0x238(%rbp), %rdi
callq 0x5470
leaq -0x1f0(%rbp), %rdi
callq 0x24130
leaq -0x1b8(%rbp), %rdi
callq 0x6d30
leaq -0x138(%rbp), %rdi
callq 0x5e20
leaq -0x120(%rbp), %rdi
callq 0x59e0
leaq -0x88(%rbp), %rdi
callq 0x5a70
leaq -0x48(%rbp), %rdi
callq 0x5e20
leaq -0x30(%rbp), %rdi
callq 0x247a0
movq -0x50(%rbp), %rdi
callq 0x3480
nop