#include <bits/stdc++.h>
#define MP make_pair
#define PB push_back
#define int long long
#define st first
#define nd second
#define rd third
#define FOR(i, a, b) for(int i =(a); i <=(b); ++i)
#define RE(i, n) FOR(i, 1, n)
#define FORD(i, a, b) for(int i = (a); i >= (b); --i)
#define REP(i, n) for(int i = 0;i <(n); ++i)
#define VAR(v, i) __typeof(i) v=(i)
#define FORE(i, c) for(VAR(i, (c).begin()); i != (c).end(); ++i)
#define ALL(x) (x).begin(), (x).end()
#define SZ(x) ((int)(x).size())
#define __builtin_ctz __builtin_ctzll
#define __builtin_clz __builtin_clzll
#define __builtin_popcount __builtin_popcountll
using namespace std;
#ifdef LOCAL
#define debug(...) _dbg(#__VA_ARGS__, __VA_ARGS__)
#define debugv(x) {{cerr <<#x <<" = "; FORE(itt, (x)) cerr <<*itt <<", "; cerr <<"\n"; }}
#else
#define debug(...) (__VA_ARGS__)
#define debugv(x)
#define cerr if(0)cout
#endif
#define next ____next
#define prev ____prev
#define left ____left
#define hash ____hash
typedef long long ll;
typedef long double LD;
typedef pair<int, int> PII;
typedef pair<ll, ll> PLL;
typedef vector<int> VI;
typedef vector<VI> VVI;
typedef vector<ll> VLL;
typedef vector<pair<int, int> > VPII;
typedef vector<pair<ll, ll> > VPLL;
template<class T> ostream& operator<<(ostream& out, vector<T> vec);
template<class T> ostream& operator<<(ostream& out, set<T> vec);
template<class L, class R> ostream& operator<<(ostream& out, map<L, R> vec);
template<class C> void mini(C&a4, C b4){a4=min(a4, b4); }
template<class C> void maxi(C&a4, C b4){a4=max(a4, b4); }
template<class T1, class T2>
ostream& operator<< (ostream &out, pair<T1, T2> pair) { return out << "(" << pair.first << ", " << pair.second << ")";}
template<class A, class B, class C> struct Triple { A first; B second; C third;
bool operator<(const Triple& t) const { if (st != t.st) return st < t.st; if (nd != t.nd) return nd < t.nd; return rd < t.rd; } };
template<class T> void ResizeVec(T&, vector<int>) {}
template<class T> void ResizeVec(vector<T>& vec, vector<int> sz) {
vec.resize(sz[0]); sz.erase(sz.begin()); if (sz.empty()) { return; }
for (T& v : vec) { ResizeVec(v, sz); }
}
typedef Triple<int, int, int> TIII;
template<class A, class B, class C>
ostream& operator<< (ostream &out, Triple<A, B, C> t) { return out << "(" << t.st << ", " << t.nd << ", " << t.rd << ")"; }
template<class T> ostream& operator<<(ostream& out, vector<T> vec) { out<<"("; for (auto& v: vec) out<<v<<", "; return out<<")"; }
template<class T> ostream& operator<<(ostream& out, set<T> vec) { out<<"("; for (auto& v: vec) out<<v<<", "; return out<<")"; }
template<class L, class R> ostream& operator<<(ostream& out, map<L, R> vec) { out<<"("; for (auto& v: vec) out<<v<<", "; return out<<")"; }
ostream& operator<<(ostream& out, __int128_t x) {
if (x < 0) { out<<"-"; x = -x; }
if (x == 0) { return out<<"0"; }
VI digs;
while (x) {
digs.PB(x % 10);
x /= 10;
}
reverse(ALL(digs));
for (auto d : digs) { out<<d; }
return out;
}
template<typename TH> void _dbg(const char* sdbg, TH h) { cerr<<sdbg<<"="<<h<<"\n"; }
template<typename TH, typename... TA> void _dbg(const char* sdbg, TH h, TA... t) {
while(*sdbg != ',') { cerr<<*sdbg++; } cerr<<"="<<h<<","; _dbg(sdbg+1, t...);
}
const int P = 1e9 + 7;
int spow(int a, int b) {
int r = 1;
while (b) {
if (b % 2) {
r = r * a % P;
}
a = a * a % P;
b /= 2;
}
return r;
}
const int N = 4e6 + 5;
int fact[N];
int pi2[N];
int f(int s, int d) {
if (s < 0 || d < 0) { return 0; }
return fact[s + 2 * d] * pi2[d] % P;
}
int g(int s, int set_cards, int n) {
int cards = 4 * n - set_cards;
assert ((s + cards) % 2 == 0);
int d = (cards - s) / 2;
return f(s, d);
}
int Choose2(int n) {
return n * (n - 1) / 2 % P;
}
int Choose3(int n) {
return (__int128_t)n * (n - 1) * (n - 2) / 6 % P;
}
int sum_ns;
struct Sol {
void Test() {
int n;
cin>>n;
sum_ns += n;
int was_zero = 0, was_two = 0, was_one = 0;
VI t;
RE (i, 2 * n) {
int x;
cin>>x;
t.PB(x);
if (x == 0) { was_zero = 1; }
if (x == 1) { was_one = 1; }
if (x == 2) { was_two = 1; }
}
if (was_two && was_zero) {
cout<<"0\n";
return;
}
if (!was_two && !was_zero) {
int res = (2 * n * n % P * (n - 1) % P * f(3, 2 * n - 3) % P + (2 * n * n % P * f(1, 2 * n - 2))) % P;
cout<<res<<"\n";
return;
}
if (!was_one) {
int res = n * f(0, 2 * n - 1) + n * (n - 1) % P * f(2, 2 * n - 2);
cout<<res % P<<"\n";
return;
}
if (was_zero) {
REP (i, 2 * n) {
t[i] = 2 - t[i];
}
t.PB(t[0]);
t.erase(t.begin());
}
//debug(t);
int any = 0;
REP (i, 2 * n - 1) {
if (t[i] == 1 && t[i + 1] == 2) {
any = i + 1;
break;
}
}
//debug(any);
if (any % 2 == 1) {
cout<<"0\n";
return;
}
REP (j, any) {
t.PB(t[j]);
}
//debug(t);
t.erase(t.begin(), t.begin() + any);
VI bloki;
assert(t[0] == 2 && t.back() == 1);
t.PB(2);
int cur_blok = 1;
REP (i, 2 * n) {
if (t[i] != t[i + 1]) {
bloki.PB(cur_blok);
cur_blok = 1;
} else {
cur_blok++;
}
}
assert(cur_blok == 1);
//debug(bloki);
for (auto blok : bloki) {
if (blok % 2 == 0) {
cout<<"0\n";
return;
}
}
int B = SZ(bloki);
// najpierw blok dwojek, potem blok jedynek
VI ones_blocks, twos_blocks;
for (int i = 0; i < B; i++) {
if (i % 2 == 0) {
twos_blocks.PB(bloki[i]);
} else {
ones_blocks.PB(bloki[i]);
}
}
assert(B % 2 == 0);
int res = 0;
int easy1 = 0, easy2 = 0;
int hard1 = 0, hard2 = 0, hard3 = 0, hard4 = 0;
for (auto blok : twos_blocks) { // bloki dwojek, liczymy AAPAPA
int pos = (blok - 1) / 2;
int here = Choose2(pos) * g(B + 2, B + 2, n) % P;
res = (res + here) % P;
easy1 = (easy1 + here) % P;
}
//debug(easy1);
for (auto blok : ones_blocks) { // bloki jedynek, liczymy PPAPAPA
int posP = (blok - 1) / 2;
int here = Choose3(posP + 1) * g(B + 3, B + 3, n) % P;
res = (res + here) % P;
easy2 = (easy2 + here) % P;
}
//debug(easy2);
for (auto blok : twos_blocks) {
int set_as = B / 2;
int fixed_intv = 2 * n - blok + 1;
int free_as = fixed_intv / 2 - set_as;
int here = set_as * g(B - 1, B + 1, n) % P + free_as * g(B + 1, B + 1, n);
here %= P;
res = (res + here) % P;
hard1 = (hard1 + here) % P;
}
//debug(hard1);
for (auto blok : ones_blocks) {
int pairs_cnt = blok / 2;
int choose_AP = Choose2(pairs_cnt + 1);
int set_ps = B / 2;
int fixed_intv = 2 * n - blok + 1;
int free_ps = fixed_intv / 2 - set_ps;
//debug(choose_AP, g(B + 1, B + 3, n), set_ps + 1);
int place_app1 = choose_AP * g(B + 1, B + 3, n) % P * (set_ps + 1) % P; // wolne P sie naklada z jakims innym (byc moze tym ostatnim)
int place_app2 = choose_AP * g(B + 3, B + 3, n) % P * free_ps % P; // wolne P sie nie naklada z nikim i jest w zafiksowanym przedziale
int choose_APP = Choose3(pairs_cnt + 1);
int place_app3 = choose_APP * g(B + 3, B + 3, n) % P; // w nieznanym przedziale mamy APP
int place_app4 = place_app3; // w nieznanym przedziale mamy PAP
//debug(place_app1, place_app2, place_app3, place_app4);
int here = (place_app1 + place_app2 + place_app3 + place_app4) % P;
res = (res + here) % P;
hard2 = (hard2 + here) % P;
}
//debug(hard2);
for (auto blok : twos_blocks) {
int set_as = B / 2;
int fixed_intv = 2 * n - blok + 1;
int free_as = fixed_intv / 2 - set_as;
int choose_A = blok / 2;
int choose_AA = Choose2(blok / 2);
int place_aa1 = choose_A * g(B, B + 2, n) % P * (set_as + 1) % P; // wolne A sie naklada z jakims innym
int place_aa2 = choose_A * g(B + 2, B + 2, n) % P * free_as % P; // wolne A sie nie naklada z nikim i jest w zafiksowanym przedziale
int place_aa3 = choose_AA * g(B + 2, B + 2, n) % P; // w nieznanym przedziale mamy AA;
int here = (place_aa1 + place_aa2 + place_aa3) % P;
res = (res + here) % P;
hard3 = (hard3 + here) % P;
}
//debug(hard3);
for (auto blok : ones_blocks) {
int set_ps = B / 2;
int fixed_intv = 2 * n - blok + 1;
int free_ps = fixed_intv / 2 - set_ps;
int pairs_cnt = blok / 2;
int choose_A = pairs_cnt;
int choose_PA = Choose2(pairs_cnt);
int place_pa1 = choose_A * g(B, B + 2, n) % P * set_ps % P; // wolne P sie naklada z jakims innym
int place_pa2 = choose_A * g(B + 2, B + 2, n) % P * free_ps % P; // wolne P sie nie naklada z nikim i jest w zafiksowanym przedziale
int place_pa3 = choose_PA * g(B + 2, B + 2, n) % P; // w nieznanym przedziale mamy PA
int here = (place_pa1 + place_pa2 + place_pa3) % P;
res = (res + here) % P;
hard4 = (hard4 + here) % P;
}
//debug(hard4);
cout<<res<<endl;
//cerr<<"?\n";
}
};
int32_t main() {
ios_base::sync_with_stdio(0);
cout << fixed << setprecision(10);
cerr << fixed << setprecision(10);
cin.tie(0);
//double beg_clock = 1.0 * clock() / CLOCKS_PER_SEC;
pi2[0] = 1;
fact[0] = 1;
int i2 = (P + 1) / 2;
RE (i, N - 1) {
fact[i] = i * fact[i - 1] % P;
pi2[i] = pi2[i - 1] * i2 % P;
}
int t;
cin>>t;
RE (i, t) {
Sol sol;
sol.Test();
}
debug(sum_ns);
return 0;
}
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325 326 327 | #include <bits/stdc++.h> #define MP make_pair #define PB push_back #define int long long #define st first #define nd second #define rd third #define FOR(i, a, b) for(int i =(a); i <=(b); ++i) #define RE(i, n) FOR(i, 1, n) #define FORD(i, a, b) for(int i = (a); i >= (b); --i) #define REP(i, n) for(int i = 0;i <(n); ++i) #define VAR(v, i) __typeof(i) v=(i) #define FORE(i, c) for(VAR(i, (c).begin()); i != (c).end(); ++i) #define ALL(x) (x).begin(), (x).end() #define SZ(x) ((int)(x).size()) #define __builtin_ctz __builtin_ctzll #define __builtin_clz __builtin_clzll #define __builtin_popcount __builtin_popcountll using namespace std; #ifdef LOCAL #define debug(...) _dbg(#__VA_ARGS__, __VA_ARGS__) #define debugv(x) {{cerr <<#x <<" = "; FORE(itt, (x)) cerr <<*itt <<", "; cerr <<"\n"; }} #else #define debug(...) (__VA_ARGS__) #define debugv(x) #define cerr if(0)cout #endif #define next ____next #define prev ____prev #define left ____left #define hash ____hash typedef long long ll; typedef long double LD; typedef pair<int, int> PII; typedef pair<ll, ll> PLL; typedef vector<int> VI; typedef vector<VI> VVI; typedef vector<ll> VLL; typedef vector<pair<int, int> > VPII; typedef vector<pair<ll, ll> > VPLL; template<class T> ostream& operator<<(ostream& out, vector<T> vec); template<class T> ostream& operator<<(ostream& out, set<T> vec); template<class L, class R> ostream& operator<<(ostream& out, map<L, R> vec); template<class C> void mini(C&a4, C b4){a4=min(a4, b4); } template<class C> void maxi(C&a4, C b4){a4=max(a4, b4); } template<class T1, class T2> ostream& operator<< (ostream &out, pair<T1, T2> pair) { return out << "(" << pair.first << ", " << pair.second << ")";} template<class A, class B, class C> struct Triple { A first; B second; C third; bool operator<(const Triple& t) const { if (st != t.st) return st < t.st; if (nd != t.nd) return nd < t.nd; return rd < t.rd; } }; template<class T> void ResizeVec(T&, vector<int>) {} template<class T> void ResizeVec(vector<T>& vec, vector<int> sz) { vec.resize(sz[0]); sz.erase(sz.begin()); if (sz.empty()) { return; } for (T& v : vec) { ResizeVec(v, sz); } } typedef Triple<int, int, int> TIII; template<class A, class B, class C> ostream& operator<< (ostream &out, Triple<A, B, C> t) { return out << "(" << t.st << ", " << t.nd << ", " << t.rd << ")"; } template<class T> ostream& operator<<(ostream& out, vector<T> vec) { out<<"("; for (auto& v: vec) out<<v<<", "; return out<<")"; } template<class T> ostream& operator<<(ostream& out, set<T> vec) { out<<"("; for (auto& v: vec) out<<v<<", "; return out<<")"; } template<class L, class R> ostream& operator<<(ostream& out, map<L, R> vec) { out<<"("; for (auto& v: vec) out<<v<<", "; return out<<")"; } ostream& operator<<(ostream& out, __int128_t x) { if (x < 0) { out<<"-"; x = -x; } if (x == 0) { return out<<"0"; } VI digs; while (x) { digs.PB(x % 10); x /= 10; } reverse(ALL(digs)); for (auto d : digs) { out<<d; } return out; } template<typename TH> void _dbg(const char* sdbg, TH h) { cerr<<sdbg<<"="<<h<<"\n"; } template<typename TH, typename... TA> void _dbg(const char* sdbg, TH h, TA... t) { while(*sdbg != ',') { cerr<<*sdbg++; } cerr<<"="<<h<<","; _dbg(sdbg+1, t...); } const int P = 1e9 + 7; int spow(int a, int b) { int r = 1; while (b) { if (b % 2) { r = r * a % P; } a = a * a % P; b /= 2; } return r; } const int N = 4e6 + 5; int fact[N]; int pi2[N]; int f(int s, int d) { if (s < 0 || d < 0) { return 0; } return fact[s + 2 * d] * pi2[d] % P; } int g(int s, int set_cards, int n) { int cards = 4 * n - set_cards; assert ((s + cards) % 2 == 0); int d = (cards - s) / 2; return f(s, d); } int Choose2(int n) { return n * (n - 1) / 2 % P; } int Choose3(int n) { return (__int128_t)n * (n - 1) * (n - 2) / 6 % P; } int sum_ns; struct Sol { void Test() { int n; cin>>n; sum_ns += n; int was_zero = 0, was_two = 0, was_one = 0; VI t; RE (i, 2 * n) { int x; cin>>x; t.PB(x); if (x == 0) { was_zero = 1; } if (x == 1) { was_one = 1; } if (x == 2) { was_two = 1; } } if (was_two && was_zero) { cout<<"0\n"; return; } if (!was_two && !was_zero) { int res = (2 * n * n % P * (n - 1) % P * f(3, 2 * n - 3) % P + (2 * n * n % P * f(1, 2 * n - 2))) % P; cout<<res<<"\n"; return; } if (!was_one) { int res = n * f(0, 2 * n - 1) + n * (n - 1) % P * f(2, 2 * n - 2); cout<<res % P<<"\n"; return; } if (was_zero) { REP (i, 2 * n) { t[i] = 2 - t[i]; } t.PB(t[0]); t.erase(t.begin()); } //debug(t); int any = 0; REP (i, 2 * n - 1) { if (t[i] == 1 && t[i + 1] == 2) { any = i + 1; break; } } //debug(any); if (any % 2 == 1) { cout<<"0\n"; return; } REP (j, any) { t.PB(t[j]); } //debug(t); t.erase(t.begin(), t.begin() + any); VI bloki; assert(t[0] == 2 && t.back() == 1); t.PB(2); int cur_blok = 1; REP (i, 2 * n) { if (t[i] != t[i + 1]) { bloki.PB(cur_blok); cur_blok = 1; } else { cur_blok++; } } assert(cur_blok == 1); //debug(bloki); for (auto blok : bloki) { if (blok % 2 == 0) { cout<<"0\n"; return; } } int B = SZ(bloki); // najpierw blok dwojek, potem blok jedynek VI ones_blocks, twos_blocks; for (int i = 0; i < B; i++) { if (i % 2 == 0) { twos_blocks.PB(bloki[i]); } else { ones_blocks.PB(bloki[i]); } } assert(B % 2 == 0); int res = 0; int easy1 = 0, easy2 = 0; int hard1 = 0, hard2 = 0, hard3 = 0, hard4 = 0; for (auto blok : twos_blocks) { // bloki dwojek, liczymy AAPAPA int pos = (blok - 1) / 2; int here = Choose2(pos) * g(B + 2, B + 2, n) % P; res = (res + here) % P; easy1 = (easy1 + here) % P; } //debug(easy1); for (auto blok : ones_blocks) { // bloki jedynek, liczymy PPAPAPA int posP = (blok - 1) / 2; int here = Choose3(posP + 1) * g(B + 3, B + 3, n) % P; res = (res + here) % P; easy2 = (easy2 + here) % P; } //debug(easy2); for (auto blok : twos_blocks) { int set_as = B / 2; int fixed_intv = 2 * n - blok + 1; int free_as = fixed_intv / 2 - set_as; int here = set_as * g(B - 1, B + 1, n) % P + free_as * g(B + 1, B + 1, n); here %= P; res = (res + here) % P; hard1 = (hard1 + here) % P; } //debug(hard1); for (auto blok : ones_blocks) { int pairs_cnt = blok / 2; int choose_AP = Choose2(pairs_cnt + 1); int set_ps = B / 2; int fixed_intv = 2 * n - blok + 1; int free_ps = fixed_intv / 2 - set_ps; //debug(choose_AP, g(B + 1, B + 3, n), set_ps + 1); int place_app1 = choose_AP * g(B + 1, B + 3, n) % P * (set_ps + 1) % P; // wolne P sie naklada z jakims innym (byc moze tym ostatnim) int place_app2 = choose_AP * g(B + 3, B + 3, n) % P * free_ps % P; // wolne P sie nie naklada z nikim i jest w zafiksowanym przedziale int choose_APP = Choose3(pairs_cnt + 1); int place_app3 = choose_APP * g(B + 3, B + 3, n) % P; // w nieznanym przedziale mamy APP int place_app4 = place_app3; // w nieznanym przedziale mamy PAP //debug(place_app1, place_app2, place_app3, place_app4); int here = (place_app1 + place_app2 + place_app3 + place_app4) % P; res = (res + here) % P; hard2 = (hard2 + here) % P; } //debug(hard2); for (auto blok : twos_blocks) { int set_as = B / 2; int fixed_intv = 2 * n - blok + 1; int free_as = fixed_intv / 2 - set_as; int choose_A = blok / 2; int choose_AA = Choose2(blok / 2); int place_aa1 = choose_A * g(B, B + 2, n) % P * (set_as + 1) % P; // wolne A sie naklada z jakims innym int place_aa2 = choose_A * g(B + 2, B + 2, n) % P * free_as % P; // wolne A sie nie naklada z nikim i jest w zafiksowanym przedziale int place_aa3 = choose_AA * g(B + 2, B + 2, n) % P; // w nieznanym przedziale mamy AA; int here = (place_aa1 + place_aa2 + place_aa3) % P; res = (res + here) % P; hard3 = (hard3 + here) % P; } //debug(hard3); for (auto blok : ones_blocks) { int set_ps = B / 2; int fixed_intv = 2 * n - blok + 1; int free_ps = fixed_intv / 2 - set_ps; int pairs_cnt = blok / 2; int choose_A = pairs_cnt; int choose_PA = Choose2(pairs_cnt); int place_pa1 = choose_A * g(B, B + 2, n) % P * set_ps % P; // wolne P sie naklada z jakims innym int place_pa2 = choose_A * g(B + 2, B + 2, n) % P * free_ps % P; // wolne P sie nie naklada z nikim i jest w zafiksowanym przedziale int place_pa3 = choose_PA * g(B + 2, B + 2, n) % P; // w nieznanym przedziale mamy PA int here = (place_pa1 + place_pa2 + place_pa3) % P; res = (res + here) % P; hard4 = (hard4 + here) % P; } //debug(hard4); cout<<res<<endl; //cerr<<"?\n"; } }; int32_t main() { ios_base::sync_with_stdio(0); cout << fixed << setprecision(10); cerr << fixed << setprecision(10); cin.tie(0); //double beg_clock = 1.0 * clock() / CLOCKS_PER_SEC; pi2[0] = 1; fact[0] = 1; int i2 = (P + 1) / 2; RE (i, N - 1) { fact[i] = i * fact[i - 1] % P; pi2[i] = pi2[i - 1] * i2 % P; } int t; cin>>t; RE (i, t) { Sol sol; sol.Test(); } debug(sum_ns); return 0; } |
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