#ifndef UNCLE
#pragma GCC optimize("O3,unroll-loops")
#endif
#include <bits/stdc++.h>
using namespace std;
#define FOR(i,p,q) for(int i=(p); i<=(q); ++i)
#define ROF(i,p,q) for(int i=(p); i>=(q); --i)
#define REP(i,q) for(int i=0; i<(q); ++i)
#define pb push_back
#define as assign
#define rz resize
#define Co const
#define al(X) X.begin(), X.end()
#define ral(X) X.rbegin(), X.rend()
#define sz(X) (int)((X).size())
#define ckmx(a,b) a=max(a,b)
#define ckmn(a,b) a=min(a,b)
#define V vector
typedef long long ll;
typedef long double ld;
typedef mt19937_64 mt;
#ifndef UNCLE
typedef basic_string<bool> vb;
typedef basic_string<int> vi;
typedef basic_string<ll> vl;
#else
typedef V<bool> vb;
typedef V<int> vi;
typedef V<ll> vl;
#endif
constexpr ll INFl=(ll)1e18+14, MD=(ll)1e9+7;
constexpr int INFi=1e9+14, MX_N=1e6+5,MX_M=MX_N*4+2;
ll Qpw(ll v,ll x){
ll pr=1;
while(x){
if(x&1) pr=(pr*v)%MD;
v=(v*v)%MD;
x/=2;
}
return pr;
}
int N,M,Q;
vl fct,rfct,pw2,rpw2;
void Prp(){
fct.as(MX_M+1,1),rfct.as(MX_M+1,1),pw2.as(MX_M+1,1),rpw2.as(MX_M+1,1);
FOR(i,1,MX_M) fct[i]=(fct[i-1]*i)%MD, pw2[i]=(pw2[i-1]*2)%MD;
rfct[MX_M]=Qpw(fct[MX_M],MD-2),rpw2[MX_M]=Qpw(pw2[MX_M],MD-2);
ROF(i,MX_M-1,0) rfct[i]=(rfct[i+1]*(i+1))%MD, rpw2[i]=(rpw2[i+1]*2)%MD;
}
inline ll Nwt(ll n,ll k)noexcept {
return ((fct[n]*rfct[k])%MD*rfct[n-k])%MD;
}
inline ll Rozd(ll dw,ll jed)noexcept {//mowie jakie zajete
if(dw+jed>2*N||dw<0||jed<0) return 0;
ll cd=2*N-dw-jed, cj=jed;
ll n=2*cd+cj;
return (((Nwt(n,cj)*fct[cj])%MD*fct[2*cd])%MD*rpw2[cd])%MD;//ig ze ok
}
inline int GtI()noexcept {
char c;
while((c=getchar_unlocked())<'0');
int pr=c-'0';
while((c=getchar_unlocked())>='0') pr=pr*10+c-'0';
return pr;
}
void PtL(ll v)noexcept {
string cs;
if(v==0) cs="0";
else{
while(v) cs.push_back(v%10+'0'),v/=10;
}
ROF(i,sz(cs)-1,0) putchar_unlocked(cs[i]);
putchar_unlocked((char)'\n');
}
void Inpt([[maybe_unused]] int ct){
N=GtI();
vi s(4*N,-1), qqt(3,0);
int qtA=1;
REP(i,2*N){
s[i]=GtI();
++qqt[s[i]];
if(s[i]==1) s[i]=0;
else s[i]=1;
if(i&&s[i]!=s[i-1]) ++qtA;
}
REP(i,2*N) s[i+2*N]=s[i];
if(qqt[0]&&qqt[2]){ PtL((ll)0); return;}
else if(qqt[0]+qqt[2]==2*N){ //zawsze wygrywam
ll rs=(N*Rozd(1,0))%MD;
if(N>=2) rs=(rs+(N*(N-1))%MD*Rozd(0,2))%MD;
PtL(rs);
return;
}
int dd=-1;
if(qqt[0]!=0) dd=0; //jaka parzystość wygrywa;
else dd=1;
if(s[0]==s[2*N-1]) --qtA;
ll rs=0;
vi ri(4*N,-1),li(4*N,INFi),mxl(4*N,INFi);
ri[4*N-1]=4*N-1;
ROF(i,4*N-2,0){
if(s[i]!=s[i+1]) ri[i]=i;
else ri[i]=ri[i+1];
}
li[0]=-1,mxl[0]=-1;
FOR(i,1,4*N-1){
if(s[i]!=s[i-1]) li[i]=i-1;
else li[i]=li[i-1];
if(li[i]==-1) mxl[i]=-1;
else{
if(!((li[i]-i)&1)) mxl[i]=li[i];
else mxl[i]=mxl[li[i]];
}
}
V<vl> rozd(2,vl(5,-1));
REP(i,2) REP(j,5) rozd[i][j]=Rozd(i,j+qtA-1);
FOR(p,0,2*N-1){
int q=p+2*N-1;
if((q&1)!=dd||s[q]==1) continue;
if(p<=mxl[q]) continue;
int qt=qtA,ls=min(ri[p],q);
if(s[p]==s[q]) ++qt;
//buduje dwa takie same, inne odemnie
ll d=ls-p,qtm=N-1-(qt>>1);
if(d>=1&&qtm>=1) rs+=(((d+1)>>1)*qtm)%MD*rozd[0][qt+2-qtA+1];//drugi sam
if(d>=1) rs+=(((d+1)>>1)*(N-qtm))%MD*rozd[1][qt-qtA+1];//drugi na kimś (jedna dwójka)
//buduje jednego nowego po prawo róznego
d=q-ls;
ll qton=qt>>1;
qtm=((d+1)>>1)-qton;
if(qtm>=1) rs+=(qtm*rozd[0][qt+1-qtA+1]);//jako nowy
if(qton>=1) rs+=(qton*rozd[1][qt-1-qtA+1]);//na kogos - wywalilem mod
rs%=MD;
}
if(qqt[0]+qqt[2]==0) rs=(rs*2)%MD;
PtL(rs);
}
signed main(){
ios_base::sync_with_stdio(0);
cin.tie(0), cout.tie(0);
Prp();
int T=1;
T=GtI();
FOR(t,1,T) Inpt(t);
}
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 | #ifndef UNCLE #pragma GCC optimize("O3,unroll-loops") #endif #include <bits/stdc++.h> using namespace std; #define FOR(i,p,q) for(int i=(p); i<=(q); ++i) #define ROF(i,p,q) for(int i=(p); i>=(q); --i) #define REP(i,q) for(int i=0; i<(q); ++i) #define pb push_back #define as assign #define rz resize #define Co const #define al(X) X.begin(), X.end() #define ral(X) X.rbegin(), X.rend() #define sz(X) (int)((X).size()) #define ckmx(a,b) a=max(a,b) #define ckmn(a,b) a=min(a,b) #define V vector typedef long long ll; typedef long double ld; typedef mt19937_64 mt; #ifndef UNCLE typedef basic_string<bool> vb; typedef basic_string<int> vi; typedef basic_string<ll> vl; #else typedef V<bool> vb; typedef V<int> vi; typedef V<ll> vl; #endif constexpr ll INFl=(ll)1e18+14, MD=(ll)1e9+7; constexpr int INFi=1e9+14, MX_N=1e6+5,MX_M=MX_N*4+2; ll Qpw(ll v,ll x){ ll pr=1; while(x){ if(x&1) pr=(pr*v)%MD; v=(v*v)%MD; x/=2; } return pr; } int N,M,Q; vl fct,rfct,pw2,rpw2; void Prp(){ fct.as(MX_M+1,1),rfct.as(MX_M+1,1),pw2.as(MX_M+1,1),rpw2.as(MX_M+1,1); FOR(i,1,MX_M) fct[i]=(fct[i-1]*i)%MD, pw2[i]=(pw2[i-1]*2)%MD; rfct[MX_M]=Qpw(fct[MX_M],MD-2),rpw2[MX_M]=Qpw(pw2[MX_M],MD-2); ROF(i,MX_M-1,0) rfct[i]=(rfct[i+1]*(i+1))%MD, rpw2[i]=(rpw2[i+1]*2)%MD; } inline ll Nwt(ll n,ll k)noexcept { return ((fct[n]*rfct[k])%MD*rfct[n-k])%MD; } inline ll Rozd(ll dw,ll jed)noexcept {//mowie jakie zajete if(dw+jed>2*N||dw<0||jed<0) return 0; ll cd=2*N-dw-jed, cj=jed; ll n=2*cd+cj; return (((Nwt(n,cj)*fct[cj])%MD*fct[2*cd])%MD*rpw2[cd])%MD;//ig ze ok } inline int GtI()noexcept { char c; while((c=getchar_unlocked())<'0'); int pr=c-'0'; while((c=getchar_unlocked())>='0') pr=pr*10+c-'0'; return pr; } void PtL(ll v)noexcept { string cs; if(v==0) cs="0"; else{ while(v) cs.push_back(v%10+'0'),v/=10; } ROF(i,sz(cs)-1,0) putchar_unlocked(cs[i]); putchar_unlocked((char)'\n'); } void Inpt([[maybe_unused]] int ct){ N=GtI(); vi s(4*N,-1), qqt(3,0); int qtA=1; REP(i,2*N){ s[i]=GtI(); ++qqt[s[i]]; if(s[i]==1) s[i]=0; else s[i]=1; if(i&&s[i]!=s[i-1]) ++qtA; } REP(i,2*N) s[i+2*N]=s[i]; if(qqt[0]&&qqt[2]){ PtL((ll)0); return;} else if(qqt[0]+qqt[2]==2*N){ //zawsze wygrywam ll rs=(N*Rozd(1,0))%MD; if(N>=2) rs=(rs+(N*(N-1))%MD*Rozd(0,2))%MD; PtL(rs); return; } int dd=-1; if(qqt[0]!=0) dd=0; //jaka parzystość wygrywa; else dd=1; if(s[0]==s[2*N-1]) --qtA; ll rs=0; vi ri(4*N,-1),li(4*N,INFi),mxl(4*N,INFi); ri[4*N-1]=4*N-1; ROF(i,4*N-2,0){ if(s[i]!=s[i+1]) ri[i]=i; else ri[i]=ri[i+1]; } li[0]=-1,mxl[0]=-1; FOR(i,1,4*N-1){ if(s[i]!=s[i-1]) li[i]=i-1; else li[i]=li[i-1]; if(li[i]==-1) mxl[i]=-1; else{ if(!((li[i]-i)&1)) mxl[i]=li[i]; else mxl[i]=mxl[li[i]]; } } V<vl> rozd(2,vl(5,-1)); REP(i,2) REP(j,5) rozd[i][j]=Rozd(i,j+qtA-1); FOR(p,0,2*N-1){ int q=p+2*N-1; if((q&1)!=dd||s[q]==1) continue; if(p<=mxl[q]) continue; int qt=qtA,ls=min(ri[p],q); if(s[p]==s[q]) ++qt; //buduje dwa takie same, inne odemnie ll d=ls-p,qtm=N-1-(qt>>1); if(d>=1&&qtm>=1) rs+=(((d+1)>>1)*qtm)%MD*rozd[0][qt+2-qtA+1];//drugi sam if(d>=1) rs+=(((d+1)>>1)*(N-qtm))%MD*rozd[1][qt-qtA+1];//drugi na kimś (jedna dwójka) //buduje jednego nowego po prawo róznego d=q-ls; ll qton=qt>>1; qtm=((d+1)>>1)-qton; if(qtm>=1) rs+=(qtm*rozd[0][qt+1-qtA+1]);//jako nowy if(qton>=1) rs+=(qton*rozd[1][qt-1-qtA+1]);//na kogos - wywalilem mod rs%=MD; } if(qqt[0]+qqt[2]==0) rs=(rs*2)%MD; PtL(rs); } signed main(){ ios_base::sync_with_stdio(0); cin.tie(0), cout.tie(0); Prp(); int T=1; T=GtI(); FOR(t,1,T) Inpt(t); } |
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