#include <bits/stdc++.h>
#define rep(a,b,c) for(auto a = (b); a != (c); a++)
#define repD(a,b,c) for(auto a = (b); a != (c); a--)
#define repIn(a, b) for(auto& a : (b))
#define repIn2(a, b, c) for(auto& [a, b] : (c))
constexpr bool dbg = 0;
#define DEBUG if constexpr(dbg)
#define DC DEBUG std::cerr
#define eol std::endl
#define int long long
#define ld long double
#define pb push_back
using namespace std;
#define rg ranges
constexpr int mod = 1e9 + 7, MAX = 4 * 1e6 + 7;
array<int, MAX> factArr;
int factUpTo;
int fact(int k) {
while(factUpTo < k) factArr[factUpTo + 1] = factArr[factUpTo] * (factUpTo + 1) % mod, factUpTo++;
return factArr[k];
}
int fastPow(int a, int x) {
if(!x) return 1;
auto h = fastPow(a, x / 2);
h = h * h % mod;
if(x & 1) h = h * a % mod;
return h;
}
array<int, MAX> twoToArr, ovTwoToArr;
void initOvTwoTo() {
twoToArr[0] = 1;
rep(i, 0, MAX - 1) twoToArr[i + 1] = twoToArr[i] * 2 % mod;
ovTwoToArr[MAX - 1] = fastPow(fastPow(2, MAX - 1), mod - 2);
repD(i, MAX - 2, -1) ovTwoToArr[i] = ovTwoToArr[i + 1] * 2 % mod;
}
int ovTwoTo(int x) {
return ovTwoToArr[x];
}
int twoTo(int x) {
return twoToArr[x];
}
void solve() {
int n;
cin >> n;
n *= 2;
vector<int> v(n);
rep(i, 0, n) cin >> v[i];
bool tw = 0, on = 0, zr = 0;
repIn(i, v) {
if(i == 0) zr = 1;
if(i == 1) on = 1;
if(i == 2) tw = 1;
}
if(tw && zr) { cout << "0\n"; return; }
if(!on) {
int ans = ((n * (n - 1) % mod) * fact(2 * n - 2) % mod) * ovTwoTo(n) % mod;
cout << ans << '\n';
return;
}
if(!zr && !tw) {
int ans = (((2 * n * n % mod) * (n - 1) % mod) * fact(2 * n - 3) % mod) * ovTwoTo(n) % mod;
cout << ans << '\n';
return;
}
int start = 0;
while(start < n && (v[start] == v[(start - 1 + n) % n] || v[start] == 1)) start++;
if(start == n) { cout << "0\n"; return; }
vector<int> v2;
rep(i, start, n) v2.pb(v[i]);
rep(i, 0, start) v2.pb(v[i]);
if(start & 1) rep(i, 0, n) v2[i] = 2 - v2[i];
repIn(i, v2) if(!i) { cout << "0\n"; return; }
int prv = -1, cntPrv = 1, cntInt = 0;
repIn(i, v2) {
if(i != prv) {
if(cntPrv & 1) prv = i, cntPrv = 0, cntInt++;
else { cout << "0\n"; return; }
}
cntPrv++;
}
DEBUG {
DC << "v2: ";
repIn(i, v2) DC << i;
DC << eol;
}
swap(v, v2);
// kurwa wzorek TODO FIX
int ans = 0, tmpPref = 0;
assert(cntInt % 2 == 0);
DC << eol;
rep(i, 0, n) {
if(v[i] == 2 && v[i + 1] == 1) {
int pref = 0;
while(i - pref + 1 && v[i - pref] == 2) pref++;
int bPrime = pref / 2;
bPrime *= 2;
int b = n - bPrime - cntInt / 2;
int rest = 2 * n - cntInt - 1;
DC << "At i = " << i << ": pref = " << pref << " ; b' = " << bPrime << " ; b = " << b << " ; rest = " << rest << "\n";
DC << " Adding " << b << " * " << fact(rest) << '\n';
DC << " And " << bPrime << " * " << (b + bPrime - 1) << " * " << fact(rest - 1) << "\n";
int twoMul = twoTo(cntInt);
DC << " All that times 2^" << cntInt << " = " << twoMul << eol;
int add = b * fact(rest) % mod;
add += bPrime * (b + bPrime - 1) % mod * fact(rest - 1) % mod;
add = add * twoMul % mod;
DC << " So add = " << add << eol;
ans = (ans + add) % mod;
}
if(v[i] == 2) continue;
if(tmpPref <= 1) while(i + tmpPref < n && v[i + tmpPref] == 1) tmpPref++;
else tmpPref--;
if(tmpPref % 2 == 1) continue;
auto pref = tmpPref;
auto aPrime = pref;
auto a = n - aPrime - cntInt / 2;
auto rest = 2 * n - cntInt - 2;
DC << "At i = " << i << ": pref = " << pref << " ; a' = " << aPrime << " ; a = " << a << " ; rest = " << rest << "\n";
DC << " Adding " << a << " * " << fact(rest) << '\n';
DC << " And " << aPrime << " * " << (a + aPrime - 1) << " * " << fact(rest - 1) << "\n";
int twoMul = twoTo(cntInt + 1);
DC << " All that times 2^" << cntInt + 1 << " = " << twoMul << eol;
int add = a * fact(rest) % mod;
add += aPrime * (a + aPrime - 1) % mod * fact(rest - 1) % mod;
add = add * twoMul % mod;
DC << " So add = " << add << eol;
ans = (ans + add) % mod;
}
cout << ans * ovTwoTo(n) % mod << '\n';
}
int32_t main() {
ios_base::sync_with_stdio(false); cin.tie(nullptr); cout.tie(nullptr);
factArr[0] = 1;
initOvTwoTo();
int t;
cin >> t;
while(t--) solve();
}
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 | #include <bits/stdc++.h> #define rep(a,b,c) for(auto a = (b); a != (c); a++) #define repD(a,b,c) for(auto a = (b); a != (c); a--) #define repIn(a, b) for(auto& a : (b)) #define repIn2(a, b, c) for(auto& [a, b] : (c)) constexpr bool dbg = 0; #define DEBUG if constexpr(dbg) #define DC DEBUG std::cerr #define eol std::endl #define int long long #define ld long double #define pb push_back using namespace std; #define rg ranges constexpr int mod = 1e9 + 7, MAX = 4 * 1e6 + 7; array<int, MAX> factArr; int factUpTo; int fact(int k) { while(factUpTo < k) factArr[factUpTo + 1] = factArr[factUpTo] * (factUpTo + 1) % mod, factUpTo++; return factArr[k]; } int fastPow(int a, int x) { if(!x) return 1; auto h = fastPow(a, x / 2); h = h * h % mod; if(x & 1) h = h * a % mod; return h; } array<int, MAX> twoToArr, ovTwoToArr; void initOvTwoTo() { twoToArr[0] = 1; rep(i, 0, MAX - 1) twoToArr[i + 1] = twoToArr[i] * 2 % mod; ovTwoToArr[MAX - 1] = fastPow(fastPow(2, MAX - 1), mod - 2); repD(i, MAX - 2, -1) ovTwoToArr[i] = ovTwoToArr[i + 1] * 2 % mod; } int ovTwoTo(int x) { return ovTwoToArr[x]; } int twoTo(int x) { return twoToArr[x]; } void solve() { int n; cin >> n; n *= 2; vector<int> v(n); rep(i, 0, n) cin >> v[i]; bool tw = 0, on = 0, zr = 0; repIn(i, v) { if(i == 0) zr = 1; if(i == 1) on = 1; if(i == 2) tw = 1; } if(tw && zr) { cout << "0\n"; return; } if(!on) { int ans = ((n * (n - 1) % mod) * fact(2 * n - 2) % mod) * ovTwoTo(n) % mod; cout << ans << '\n'; return; } if(!zr && !tw) { int ans = (((2 * n * n % mod) * (n - 1) % mod) * fact(2 * n - 3) % mod) * ovTwoTo(n) % mod; cout << ans << '\n'; return; } int start = 0; while(start < n && (v[start] == v[(start - 1 + n) % n] || v[start] == 1)) start++; if(start == n) { cout << "0\n"; return; } vector<int> v2; rep(i, start, n) v2.pb(v[i]); rep(i, 0, start) v2.pb(v[i]); if(start & 1) rep(i, 0, n) v2[i] = 2 - v2[i]; repIn(i, v2) if(!i) { cout << "0\n"; return; } int prv = -1, cntPrv = 1, cntInt = 0; repIn(i, v2) { if(i != prv) { if(cntPrv & 1) prv = i, cntPrv = 0, cntInt++; else { cout << "0\n"; return; } } cntPrv++; } DEBUG { DC << "v2: "; repIn(i, v2) DC << i; DC << eol; } swap(v, v2); // kurwa wzorek TODO FIX int ans = 0, tmpPref = 0; assert(cntInt % 2 == 0); DC << eol; rep(i, 0, n) { if(v[i] == 2 && v[i + 1] == 1) { int pref = 0; while(i - pref + 1 && v[i - pref] == 2) pref++; int bPrime = pref / 2; bPrime *= 2; int b = n - bPrime - cntInt / 2; int rest = 2 * n - cntInt - 1; DC << "At i = " << i << ": pref = " << pref << " ; b' = " << bPrime << " ; b = " << b << " ; rest = " << rest << "\n"; DC << " Adding " << b << " * " << fact(rest) << '\n'; DC << " And " << bPrime << " * " << (b + bPrime - 1) << " * " << fact(rest - 1) << "\n"; int twoMul = twoTo(cntInt); DC << " All that times 2^" << cntInt << " = " << twoMul << eol; int add = b * fact(rest) % mod; add += bPrime * (b + bPrime - 1) % mod * fact(rest - 1) % mod; add = add * twoMul % mod; DC << " So add = " << add << eol; ans = (ans + add) % mod; } if(v[i] == 2) continue; if(tmpPref <= 1) while(i + tmpPref < n && v[i + tmpPref] == 1) tmpPref++; else tmpPref--; if(tmpPref % 2 == 1) continue; auto pref = tmpPref; auto aPrime = pref; auto a = n - aPrime - cntInt / 2; auto rest = 2 * n - cntInt - 2; DC << "At i = " << i << ": pref = " << pref << " ; a' = " << aPrime << " ; a = " << a << " ; rest = " << rest << "\n"; DC << " Adding " << a << " * " << fact(rest) << '\n'; DC << " And " << aPrime << " * " << (a + aPrime - 1) << " * " << fact(rest - 1) << "\n"; int twoMul = twoTo(cntInt + 1); DC << " All that times 2^" << cntInt + 1 << " = " << twoMul << eol; int add = a * fact(rest) % mod; add += aPrime * (a + aPrime - 1) % mod * fact(rest - 1) % mod; add = add * twoMul % mod; DC << " So add = " << add << eol; ans = (ans + add) % mod; } cout << ans * ovTwoTo(n) % mod << '\n'; } int32_t main() { ios_base::sync_with_stdio(false); cin.tie(nullptr); cout.tie(nullptr); factArr[0] = 1; initOvTwoTo(); int t; cin >> t; while(t--) solve(); } |
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