#pragma GCC optimize ("Ofast")
#define _USE_MATH_DEFINES
#include <bits/stdc++.h>
#define FOR(i, a, b) for (auto i=(a); i<(b); i++)
#define FORD(i, a, b) for (auto i=(a); i>(b); i--)
#define SZ(x) ((int)(x).size())
#define ITH_BIT(m, i) ((m)>>(i) & 1)
#define PPC(x) __builtin_popcount(x)
#ifdef DEBUG
#include "debug.h"
#else
#define dbg(...) 0
#endif
template <typename T1, typename T2> inline void remin(T1& a, T2 b) { a = std::min(a, (T1)b); }
template <typename T1, typename T2> inline void remax(T1& a, T2 b) { a = std::max(a, (T1)b); }
const int maxN = 1 << 22, mod = 1'000'000'007;
template <typename T1, typename T2> inline void addMod(T1& a, T2 b) { a = (a + b) % mod; }
template <typename T1, typename T2> inline void multMod(T1& a, T2 b) { a = a * b % mod; }
long long fact[maxN], halfPow[maxN];
int n, m, segs;
int T[maxN / 2];
void precomp()
{
long long half = (mod + 1) / 2;
fact[0] = halfPow[0] = 1;
FOR(i, 1, maxN)
{
fact[i] = fact[i-1] * i % mod;
halfPow[i] = halfPow[i-1] * half % mod;
}
}
long long fillUp(int takenOnes, int takenTwos)
{
int cards = m * 2 - takenOnes - takenTwos * 2;
int freeTwos = m - takenOnes - takenTwos;
if (takenOnes + takenTwos > m)
return 0;
else
return fact[cards] * halfPow[freeTwos] % mod;
}
long long f(int newSolos, long long newSolosCombs, bool newPaired, bool additionalTheirSolo)
{
long long mult = newSolosCombs;
int ourSolos = segs + newSolos;
if (newPaired)
multMod(mult, ourSolos--);
int theirSolos = segs + additionalTheirSolo;
int solosTotal = ourSolos + theirSolos;
return mult * fillUp(solosTotal, newPaired);
}
long long profitFromPref(int suf)
{
int prefSpots = n - suf/2;
int prefSpotsOnes = segs;
int prefSpotsFree = prefSpots - prefSpotsOnes;
bool additionalMaxsSolo = suf % 2 == 0;
long long profitSolo = f(1, prefSpotsFree, false, additionalMaxsSolo);
long long profitPaired = f(0, 1, true, additionalMaxsSolo);
long long profitPref = profitSolo + profitPaired;
return profitPref;
}
long long profitFromSuf(int suf)
{
int sufSpots = suf / 2;
int spotsFree = (n - segs - 1);
long long sufSolosCombs = 1ll * sufSpots * spotsFree % mod;
bool additionalMaxsSolo = suf % 2 == 0;
long long profitSolos = f(2, sufSolosCombs, false, additionalMaxsSolo);
long long profitPaired = f(1, sufSpots, true, additionalMaxsSolo);
long long profitSuf = profitSolos + profitPaired;
return profitSuf;
}
long long profit(int suf)
{
return (profitFromPref(suf) + profitFromSuf(suf)) % mod;
}
long long resultOnMono(int x)
{
long long dominSeparated = fillUp(2, 0);
multMod(dominSeparated, n);
multMod(dominSeparated, n-1);
long long dominTogether = fillUp(0, 1) * n;
long long domin = (dominSeparated + dominTogether) % mod;
long long drawSeparated = fillUp(3, 0);
multMod(drawSeparated, m);
multMod(drawSeparated, n);
multMod(drawSeparated, n-1);
long long drawTogether = fillUp(1, 1);
multMod(drawTogether, m);
multMod(drawTogether, n);
long long draw = (drawSeparated + drawTogether) % mod;
return x == 1 ? draw : domin;
}
void solve()
{
scanf ("%d", &n);
m = n * 2, segs = 0;
int suf = 0, visMask = 0;
FOR(i, 0, m)
{
scanf ("%d", T+i);
visMask |= 1 << T[i];
}
T[m] = T[0];
if (visMask != 3 and visMask != 6)
{
long long res = (visMask & 5) == 5
? 0
: resultOnMono(T[0]);
printf("%lld\n", res);
return;
}
FORD(i, m-1, -1)
{
if (T[i] == 1 and T[i+1] != 1)
segs++;
if (T[i] != T[i+1])
suf = 0;
suf++;
}
long long res = 0;
bool dominParity = visMask & 4;
auto validMaxsSpot = [&](int i) -> bool
{
bool sufOfOnes = T[i+1] == 1;
bool sufEven = suf % 2 == 0;
bool validSuf = sufOfOnes == sufEven;
bool maxShallDomin = i % 2 == dominParity;
return T[i] == 1
and validSuf
and maxShallDomin;
};
FORD(i, m-1, -1)
{
if (validMaxsSpot(i))
res += profit(suf);
if (T[i] != T[i+1])
{
if (suf % 2 == 0)
{
res = 0;
break;
}
suf = 0;
}
suf++;
}
res %= mod;
printf("%lld\n", res);
}
int main()
{
int tc = 1;
scanf ("%d", &tc);
precomp();
FOR(cid, 1, tc+1)
{
// printf("Case #%d: ", cid);
solve();
}
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 | #pragma GCC optimize ("Ofast") #define _USE_MATH_DEFINES #include <bits/stdc++.h> #define FOR(i, a, b) for (auto i=(a); i<(b); i++) #define FORD(i, a, b) for (auto i=(a); i>(b); i--) #define SZ(x) ((int)(x).size()) #define ITH_BIT(m, i) ((m)>>(i) & 1) #define PPC(x) __builtin_popcount(x) #ifdef DEBUG #include "debug.h" #else #define dbg(...) 0 #endif template <typename T1, typename T2> inline void remin(T1& a, T2 b) { a = std::min(a, (T1)b); } template <typename T1, typename T2> inline void remax(T1& a, T2 b) { a = std::max(a, (T1)b); } const int maxN = 1 << 22, mod = 1'000'000'007; template <typename T1, typename T2> inline void addMod(T1& a, T2 b) { a = (a + b) % mod; } template <typename T1, typename T2> inline void multMod(T1& a, T2 b) { a = a * b % mod; } long long fact[maxN], halfPow[maxN]; int n, m, segs; int T[maxN / 2]; void precomp() { long long half = (mod + 1) / 2; fact[0] = halfPow[0] = 1; FOR(i, 1, maxN) { fact[i] = fact[i-1] * i % mod; halfPow[i] = halfPow[i-1] * half % mod; } } long long fillUp(int takenOnes, int takenTwos) { int cards = m * 2 - takenOnes - takenTwos * 2; int freeTwos = m - takenOnes - takenTwos; if (takenOnes + takenTwos > m) return 0; else return fact[cards] * halfPow[freeTwos] % mod; } long long f(int newSolos, long long newSolosCombs, bool newPaired, bool additionalTheirSolo) { long long mult = newSolosCombs; int ourSolos = segs + newSolos; if (newPaired) multMod(mult, ourSolos--); int theirSolos = segs + additionalTheirSolo; int solosTotal = ourSolos + theirSolos; return mult * fillUp(solosTotal, newPaired); } long long profitFromPref(int suf) { int prefSpots = n - suf/2; int prefSpotsOnes = segs; int prefSpotsFree = prefSpots - prefSpotsOnes; bool additionalMaxsSolo = suf % 2 == 0; long long profitSolo = f(1, prefSpotsFree, false, additionalMaxsSolo); long long profitPaired = f(0, 1, true, additionalMaxsSolo); long long profitPref = profitSolo + profitPaired; return profitPref; } long long profitFromSuf(int suf) { int sufSpots = suf / 2; int spotsFree = (n - segs - 1); long long sufSolosCombs = 1ll * sufSpots * spotsFree % mod; bool additionalMaxsSolo = suf % 2 == 0; long long profitSolos = f(2, sufSolosCombs, false, additionalMaxsSolo); long long profitPaired = f(1, sufSpots, true, additionalMaxsSolo); long long profitSuf = profitSolos + profitPaired; return profitSuf; } long long profit(int suf) { return (profitFromPref(suf) + profitFromSuf(suf)) % mod; } long long resultOnMono(int x) { long long dominSeparated = fillUp(2, 0); multMod(dominSeparated, n); multMod(dominSeparated, n-1); long long dominTogether = fillUp(0, 1) * n; long long domin = (dominSeparated + dominTogether) % mod; long long drawSeparated = fillUp(3, 0); multMod(drawSeparated, m); multMod(drawSeparated, n); multMod(drawSeparated, n-1); long long drawTogether = fillUp(1, 1); multMod(drawTogether, m); multMod(drawTogether, n); long long draw = (drawSeparated + drawTogether) % mod; return x == 1 ? draw : domin; } void solve() { scanf ("%d", &n); m = n * 2, segs = 0; int suf = 0, visMask = 0; FOR(i, 0, m) { scanf ("%d", T+i); visMask |= 1 << T[i]; } T[m] = T[0]; if (visMask != 3 and visMask != 6) { long long res = (visMask & 5) == 5 ? 0 : resultOnMono(T[0]); printf("%lld\n", res); return; } FORD(i, m-1, -1) { if (T[i] == 1 and T[i+1] != 1) segs++; if (T[i] != T[i+1]) suf = 0; suf++; } long long res = 0; bool dominParity = visMask & 4; auto validMaxsSpot = [&](int i) -> bool { bool sufOfOnes = T[i+1] == 1; bool sufEven = suf % 2 == 0; bool validSuf = sufOfOnes == sufEven; bool maxShallDomin = i % 2 == dominParity; return T[i] == 1 and validSuf and maxShallDomin; }; FORD(i, m-1, -1) { if (validMaxsSpot(i)) res += profit(suf); if (T[i] != T[i+1]) { if (suf % 2 == 0) { res = 0; break; } suf = 0; } suf++; } res %= mod; printf("%lld\n", res); } int main() { int tc = 1; scanf ("%d", &tc); precomp(); FOR(cid, 1, tc+1) { // printf("Case #%d: ", cid); solve(); } return 0; } |
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