求证伪或hack（玄关）

#include <bits/stdc++.h>
using namespace std;
#define int long long
const int N=3e5+10;
int v[N],t1,t2,t3,cnt;
void check(int x){
	if(x==0) return;
	if(x==1) ++t1;
	if(x==2) ++t2;
	if(x==3){
		if(t1) ++cnt,--t1;
		else ++t3;
	}
	if(x==4) ++cnt;
	if(x<=4) return;
	int now=x/3;
	if(now%2) --now;
	if(now/2>=t2){
		cnt+=t2*2;
		x-=t2*6;
		t2=0;
	} 
	else{
		t2-=now/2;
		cnt+=now;
		x-=now*3;
	}
	if(t2&&x>=3){
		x-=3,t2--,t1++,++cnt;
	}
	if(t3){
		if(t3>=t1) t3-=t1;
		if(t3>=x) t3-=x,cnt+=x,x=0;
		else cnt+=t3,x-=t3,t3=0;
	} 
	int k=x/4;
	cnt+=k;
	x-=k*4;
	if(x==3) ++t3;
	else if(x==2) ++t2;
	else if(x==1) ++t1;
	return;
}
signed main(){
	//freopen("card3.in","r",stdin);
	//freopen("card3.out","w",stdout);
	int T;cin>>T;
	while(T--){
		int n;cin>>n;
		for(int i=1;i<=n;i++){
			cin>>v[i];
		}
		sort(v+1,v+n+1);
		t1=t2=t3=cnt=0;
		for(int i=1;i<=n;i++){
			if(v[i]<=4){
				check(v[i]);
				continue;
			}
			if(t1){
				/*if((v[i]-4)%3==0){
					int now=(v[i]-4)/3;
					if(now<t1){
						t1-=now;
						cnt+=now+1;
					}
					else{
						cnt+=t1;
						v[i]-=t1*3;
						t1=0;
						check(v[i]);
					}
					continue;
				}*/
				int now=v[i]/3;
				if(now<t1){
					cnt+=now;
					t1-=now;
					v[i]-=now*3;
					check(v[i]);
				}
				else{	
					cnt+=t1;
					v[i]-=t1*3;
					t1=0;
					check(v[i]);
				}
				continue;
			}
			check(v[i]);
		}
		//cout<<t1<<" "<<t2<<" "<<t3<<endl;
		if(t3>=t1) cnt+=t1,t3-=t1,t1=0;
		else cnt+=t3,t1-=t3,t3=0;
		if(!t3) cnt+=t1+t2;
		else{
			if(t3/2>=t2){
				cnt+=t2;
				t3-=t2*2;
				cnt+=(t3/4)*3;
				if(t3%4==1||t3%4==2) cnt+=2;
				else if(t3%4==3) cnt+=3;
			}
			else{
				cnt+=t3/2*2;
				t2-=t3/2;
				if(t3%2) ++cnt;
				cnt+=t2;
			}
		}
		cout<<cnt<<endl;
	}
	return 0;
}