#include <bits/stdc++.h>
using namespace std;
#define pb push_back
#define st first
#define nd second
typedef long long ll;
typedef long double ld;
const ll I = 1'000'000'000'000'000'000LL;
const int II = 2'000'000'000;
const ll M = 1'000'000'007LL;
const int N = 1'000'007;
int tab[4 * N];
int nxt[4 * N], il[4 * N][2];
ll sil[4 * N];
void Pre(int n)
{
sil[0] = 1LL;
for(int i = 1; i <= n; ++i)
sil[i] = (sil[i - 1] * (ll)i) % M;
}
ll QP(ll a, ll n)
{
ll ans = 1LL;
while(n > 0LL)
{
if(n % 2LL == 1LL)
ans = (ans * a) % M;
a = (a * a) % M;
n /= 2LL;
}
return ans;
}
ll C(ll il, ll il2)
{
return (sil[il] * QP(QP(2, il2), M - 2LL)) % M;
}
void Solve()
{
int n;
int cz0 = 0, cz1 = 0, cz2 = 0;
cin >> n;
for(int i = 1; i <= 2 * n; ++i)
{
cin >> tab[i];
if(tab[i] == 0) cz0 = 1;
if(tab[i] == 1) cz1 = 1;
if(tab[i] == 2) cz2 = 1;
}
if(cz0 && cz2)
{
cout << 0 << "\n";
return;
}
if(cz1 == 0)
{
ll ans = (ll)n * C(n * 4 - 2, 2 * n - 1);
ans += (((ll)n * (ll)(n - 1)) % M) * C(n * 4 - 2, 2 * n - 2);
ans %= M;
cout << ans << "\n";
return;
}
if(cz0)
for(int i = 1; i <= 2 * n; ++i)
tab[i] = 2 - tab[i];
else
for(int i = 2; i <= 2 * n; ++i)
swap(tab[1], tab[i]);
for(int i = 1; i <= 2 * n; ++i)
tab[i + 2 * n] = tab[i];
for(int i = 4 * n; i >= 1; --i)
{
nxt[i] = i + 1;
if(tab[i] == tab[i + 1])
nxt[i] = nxt[i + 1];
else
++il[i][(i + tab[i]) % 2];
nxt[i] = min(nxt[i], i + 2 * n - 1);
}
for(int i = 1; i <= 4 * n; ++i)
for(int r = 0; r < 2; ++r)
il[i][r] += il[i - 1][r];
ll ans = 0LL;
for(int i = 1; i <= 2 * n; i += 2)
{
if(tab[i] != 1) continue;
int ar = (tab[i] + i) % 2;
int ils = il[i + 2 * n - 1][ar] - il[i][ar] + 1;
if((il[i + 2 * n - 1][ar ^ 1] - il[i - 1][ar ^ 1]) > 0) continue;
// cout << "\nC: " << i << " " << ils << "\n";
int d = nxt[i + 1] - i - 1;
ll ilp = ((d + (tab[i + 1] % 2)) / 2LL);
ll p1 = (ils) / 2LL;
ll p2 = (n - ilp) - p1;
// cout << d << " " << ilp << " " << p1 << " " << p2 << "\n";
ans += ilp * C(4 * n - ils - 2, 2 * n - ils - 1);
ans += ((ilp * (ll)(n - p1 - 1)) % M) * C(4 * n - ils - 2, 2 * n - ils - 2);
ans += ((ilp * (ll)(p1)) % M) * C(4 * n - ils - 2, 2 * n - ils - 1);
ans %= M;
ans += p1 * C(4 * n - ils - 1, 2 * n - ils);
ans += p2 * C(4 * n - ils - 1, 2 * n - ils - 1);
ans %= M;
}
if(cz0 == 0 && cz2 == 0)
ans = (ans * 2LL) % M;
cout << ans << "\n";
for(int i = 1; i <= 4 * n; ++i)
for(int r = 0; r < 2; ++r)
il[i][r] = 0;
}
int main()
{
Pre(4*1000*1000+4);
ios_base::sync_with_stdio(false);
cin.tie(nullptr);
int t; cin >> t;
while(t--)
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 | #include <bits/stdc++.h> using namespace std; #define pb push_back #define st first #define nd second typedef long long ll; typedef long double ld; const ll I = 1'000'000'000'000'000'000LL; const int II = 2'000'000'000; const ll M = 1'000'000'007LL; const int N = 1'000'007; int tab[4 * N]; int nxt[4 * N], il[4 * N][2]; ll sil[4 * N]; void Pre(int n) { sil[0] = 1LL; for(int i = 1; i <= n; ++i) sil[i] = (sil[i - 1] * (ll)i) % M; } ll QP(ll a, ll n) { ll ans = 1LL; while(n > 0LL) { if(n % 2LL == 1LL) ans = (ans * a) % M; a = (a * a) % M; n /= 2LL; } return ans; } ll C(ll il, ll il2) { return (sil[il] * QP(QP(2, il2), M - 2LL)) % M; } void Solve() { int n; int cz0 = 0, cz1 = 0, cz2 = 0; cin >> n; for(int i = 1; i <= 2 * n; ++i) { cin >> tab[i]; if(tab[i] == 0) cz0 = 1; if(tab[i] == 1) cz1 = 1; if(tab[i] == 2) cz2 = 1; } if(cz0 && cz2) { cout << 0 << "\n"; return; } if(cz1 == 0) { ll ans = (ll)n * C(n * 4 - 2, 2 * n - 1); ans += (((ll)n * (ll)(n - 1)) % M) * C(n * 4 - 2, 2 * n - 2); ans %= M; cout << ans << "\n"; return; } if(cz0) for(int i = 1; i <= 2 * n; ++i) tab[i] = 2 - tab[i]; else for(int i = 2; i <= 2 * n; ++i) swap(tab[1], tab[i]); for(int i = 1; i <= 2 * n; ++i) tab[i + 2 * n] = tab[i]; for(int i = 4 * n; i >= 1; --i) { nxt[i] = i + 1; if(tab[i] == tab[i + 1]) nxt[i] = nxt[i + 1]; else ++il[i][(i + tab[i]) % 2]; nxt[i] = min(nxt[i], i + 2 * n - 1); } for(int i = 1; i <= 4 * n; ++i) for(int r = 0; r < 2; ++r) il[i][r] += il[i - 1][r]; ll ans = 0LL; for(int i = 1; i <= 2 * n; i += 2) { if(tab[i] != 1) continue; int ar = (tab[i] + i) % 2; int ils = il[i + 2 * n - 1][ar] - il[i][ar] + 1; if((il[i + 2 * n - 1][ar ^ 1] - il[i - 1][ar ^ 1]) > 0) continue; // cout << "\nC: " << i << " " << ils << "\n"; int d = nxt[i + 1] - i - 1; ll ilp = ((d + (tab[i + 1] % 2)) / 2LL); ll p1 = (ils) / 2LL; ll p2 = (n - ilp) - p1; // cout << d << " " << ilp << " " << p1 << " " << p2 << "\n"; ans += ilp * C(4 * n - ils - 2, 2 * n - ils - 1); ans += ((ilp * (ll)(n - p1 - 1)) % M) * C(4 * n - ils - 2, 2 * n - ils - 2); ans += ((ilp * (ll)(p1)) % M) * C(4 * n - ils - 2, 2 * n - ils - 1); ans %= M; ans += p1 * C(4 * n - ils - 1, 2 * n - ils); ans += p2 * C(4 * n - ils - 1, 2 * n - ils - 1); ans %= M; } if(cz0 == 0 && cz2 == 0) ans = (ans * 2LL) % M; cout << ans << "\n"; for(int i = 1; i <= 4 * n; ++i) for(int r = 0; r < 2; ++r) il[i][r] = 0; } int main() { Pre(4*1000*1000+4); ios_base::sync_with_stdio(false); cin.tie(nullptr); int t; cin >> t; while(t--) Solve(); return 0; } |
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