int rec(int nodes, bits &curr, bits &pool, bits &excl) {
if (pool.none() && excl.none()) {
return curr.count();
}
int ans = 0, u = 0;
for (int v = 0; v < nodes; v++) {
if (pool[v] || excl[v]) {
u = v;
}
}
for (int v = 0; v < nodes; v++) {
if (!pool[v] || adj[u][v]) {
continue;
}
bits ncurr, npool, nexcl;
for (int i = 0; i < nodes; i++) {
ncurr[i] = curr[i];
}
ncurr[v] = true;
for (int j = 0; j < nodes; j++) {
npool[j] = pool[j] && adj[v][j];
nexcl[j] = excl[j] && adj[v][j];
}
ans = std::max(ans, rec(nodes, ncurr, npool, nexcl));
pool[v] = false;
excl[v] = true;
}
return ans;
}
void take2(int pos, bits &ret) {
ret.set(pos);
for(int i=0;i<N-1;i++) {
if(rela[i].first == pos && !ret.test(rela[i].second)) {
take2(rela[i].second, ret);
}
if(rela[i].second == pos && !ret.test(rela[i].first)) {
take2(rela[i].first, ret);
}
}
}
void take(int pos, int no, bits &ret) {
ret.set(pos);
for(int i=0;i<N-1;i++) {
if(rela[i].first == pos && rela[i].second != no) {
take2(rela[i].second, ret);
}
if(rela[i].second == pos && rela[i].first != no) {
take2(rela[i].first, ret);
}
}
ret.reset(pos);
}
int go(bits &st) {
if(memo.count(st)) {
return memo[st];
}
bits candi = st;
int cnt = candi.count();
if(cnt == 0) return 1;
for(int i=0;i<N-1;i++) {
int p1 = rela[i].first;
int p2 = rela[i].second;
if(!st.test(p1) || !st.test(p2)) continue;
candi.reset(p2);
}
long long rett = 0;
for(int i=0;i<N;i++) {
if(candi.test(i)) {
long long ret = 1;
int cnt2 = cnt-1;
for(int j=0;j<N-1;j++) {
if(rela[j].first == i) {
bits tmp;
take(rela[j].second, i, tmp);
tmp.set(rela[j].second);
for(int k=0;k<N;k++) {
if(tmp.test(k) && !st.test(k))
tmp.reset(k);
}
int tmp2 = tmp.count();
ret *= combi[cnt2][tmp2];
cnt2 -= tmp2;
ret %= 1000000007;
ret *= go(tmp);
ret %= 1000000007;
}
}
rett += ret;
rett %= 1000000007;
}
}
memo[st] = rett;
}
static inline bool iddfs(bits state, val const res, val const rem, val const d) {
if (rem == 0)
return true;
if (memed(state))
return false;
if (rem > d)
return false;
num[d] = res;
bits was_processed = state;
defrd_size[d] = 0;
for (val k = d; k <= start_d; ++k) {
val const i = num[k];
for (val j = start_d; j > k; --j) {
val const rhs = num[j];
val const sum = i + rhs;
if (sum <= max_n && process(was_processed, state, sum, rem, d, add, i, rhs))
return true;
val const diff = abs(i - rhs);
if (process(was_processed, state, diff, rem, d, sub, max(i, rhs), min(i, rhs)))
return true;
}
for (val j = 2*i, p = 1; j <= max_n; j *= 2, ++p)
if (process(was_processed, state, j, rem, d, shift, i, p))
return true;
}
for (val l = 0; l < defrd_size[d]; ++l) {
action const &defrd = deferred[d][l];
state.set(defrd.res);
if(iddfs(state, defrd.res, rem, d - 1)) {
result[d] = defrd;
return true;
}
state.reset(defrd.res);
}
return false;
}
static inline bool process(bits &was_processed, bits state, val const j,
val const rem, val const d,
char const *const actname, val const lhs, val const rhs) {
if (was_processed.test(j))
return false;
was_processed.set(j);
if (target.test(j)) {
state.set(j);
if (iddfs(state, j, rem - 1, d - 1)) {
result[d].name = actname;
result[d].lhs = lhs;
result[d].rhs = rhs;
return true;
}
return false;
}
action &defrd = deferred[d][defrd_size[d]];
defrd.name = actname;
defrd.lhs = lhs;
defrd.rhs = rhs;
defrd.res = j;
++defrd_size[d];
return false;
}
static inline bool memed(bits const state) {
unsigned long long const i = (state.to_ullong() * 2038074743) % mem_size;
bool const already_in = mem[i] == state;
mem[i] = state;
return already_in;
}