#include <bits/stdc++.h>
using namespace std;
using ll = long long;

int main(){
	int T;cin>>T;

	while(T--){
		int N;cin>>N;
		vector<ll>A(N);
		for(int i=0;i<N;i++){cin>>A[i];}

		multiset<tuple<ll,int,int,int>>pq;
		vector<int>L(N),R(N);
		for(int i=0;i<N;i++){
			pq.insert({A[i],i,(i-1+N)%N,(i+1)%N});
			L[i]=(i-1+N)%N;
			R[i]=(i+1)%N;
		}

		ll ans=0;

		auto solve=[&](int l,int r){
			if(pq.size()==2){
				ans+=min(A[l],A[r]);
				pq.erase(pq.begin());
				return;
			}

			assert(L[r]==l&&R[l]==r);
			int rr=R[r];

			pq.erase(pq.find({A[l],l,L[l],R[l]}));
			pq.erase(pq.find({A[r],r,L[r],R[r]}));
			pq.erase(pq.find({A[rr],rr,L[rr],R[rr]}));

			ans+=min(A[l],A[r]);
			A[l]+=A[r];

			R[l]=rr;
			L[rr]=l;
			pq.insert({A[l],l,L[l],R[l]});
			pq.insert({A[rr],rr,L[rr],R[rr]});
		};

		while(pq.size()>1){
			auto tup=*pq.begin();
			auto[ai,i,l,r]=tup;
			//cerr<<pq.size()<<'\n';
			//cerr<<ai<<' '<<i<<' '<<l<<' '<<r<<"\n\n";

			if(A[l]<A[r]){
				solve(l,i);
			}

			else{
				solve(i,r);
			}
		}

		cout<<ans<<'\n';
	}
}