Problem: Taro loves chocolate and when he returns from school he eats his favorite chocolate bar with a heart symbol on it. A recent pleasure is to eat all the heart symbol blocks to the end. Taro , Try to eat as many heartless blocks as possible, with all heartmark blocks connected.

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However, Taro is still young, and even if he tries to eat as above, useless blocks will remain. Therefore, Taro seeks the maximum number of blocks that can be eaten when all the heart-shaped blocks are left connected. I asked you to create a program.

Taro can eat whatever way he wants, as long as all the heart-shaped blocks are connected. If one side of one block does not touch the other block, it will be separated.



Input

The input consists of multiple datasets, each dataset given in the following format:


H W
H x W numbers


H and W are integers indicating the vertical size and horizontal size of the chocolate bar, respectively. H x W numbers represent block information, '0' representing blocks without a heart mark, and blocks with a heart mark. Consists of '1'.

The end of the input is indicated by the dataset where H = W = 0. Do not output for this case.

You can assume that 1 ≤ H, W ≤ 12 and the number of heart-shaped blocks is 6 or less.

Output

For each dataset, output the maximum number of blocks that Taro can eat.

Example

Input

4 4
1 0 0 0
0 0 1 0
0 1 0 0
1 0 0 1
1 1
1
2 3
1 0 0
0 0 1
0 0


Output

7
0
2

Solution (in CPP):

Solution:
#include <cassert>// c
#include <iostream>// io
#include <iomanip>
#include <fstream>
#include <sstream>
#include <vector>// container
#include <map>
#include <set>
#include <queue>
#include <bitset>
#include <stack>
#include <algorithm>// other
#include <complex>
#include <numeric>
#include <functional>
#include <random>
#include <regex>
using namespace std;

typedef long long  ll;

#define ALL(c) (begin(c)),(end(c))
#define REP(i,n) FOR(i,0,n)
#define REPr(i,n) FORr(i,0,n)
#define FOR(i,l,r) for(int i=(int)(l);i<(int)(r);++i)
#define FORr(i,l,r) for(int i=(int)(r)-1;i>=(int)(l);--i)
#define EACH(it,o) for(auto it = (o).begin(); it != (o).end(); ++it)
#define IN(l,v,r) ((l)<=(v) && (v)<(r))
#define UNIQUE(v) v.erase(unique(ALL(v)),v.end())
//debug
#define DUMP(x)  cerr << #x << " = " << (x)
#define LINE()    cerr<< " (L" << __LINE__ << ")"

class range {
private:
	struct Iter{
		int v;
		int operator*(){return v;}
		bool operator!=(Iter& itr) {return v < itr.v;}
		void operator++() {++v;}
	};
	Iter i, n;
public:
	range(int n) : i({0}), n({n}) {}
	range(int i, int n) : i({i}), n({n}) {}
	Iter& begin() {return i;}
	Iter& end() {return n;}
};

//output
template<typename T> ostream& operator << (ostream& os, const vector<T>& as){REP(i,as.size()){if(i!=0)os<<" "; os<<as[i];}return os;}
template<typename T> ostream& operator << (ostream& os, const vector<vector<T>>& as){REP(i,as.size()){if(i!=0)os<<endl; os<<as[i];}return os;}
template<typename T> ostream& operator << (ostream& os, const set<T>& ss){for(auto a:ss){if(a!=ss.begin())os<<" "; os<<a;}return os;}
template<typename T1,typename T2> ostream& operator << (ostream& os, const pair<T1,T2>& p){os<<p.first<<" "<<p.second;return os;}
template<typename K,typename V> ostream& operator << (ostream& os, const map<K,V>& m){bool isF=true;for(auto& p:m){if(!isF)os<<endl;os<<p;isF=false;}return os;}
template<typename T1> ostream& operator << (ostream& os, const tuple<T1>& t){os << get<0>(t);return os;}
template<typename T1,typename T2> ostream& operator << (ostream& os, const tuple<T1,T2>& t){os << get<0>(t)<<" "<<get<1>(t);return os;}
template<typename T1,typename T2,typename T3> ostream& operator << (ostream& os, const tuple<T1,T2,T3>& t){os << get<0>(t)<<" "<<get<1>(t)<<" "<<get<2>(t);return os;}
template<typename T1,typename T2,typename T3,typename T4> ostream& operator << (ostream& os, const tuple<T1,T2,T3,T4>& t){os << get<0>(t)<<" "<<get<1>(t)<<" "<<get<2>(t)<<" "<<get<3>(t);return os;}
template<typename T1,typename T2,typename T3,typename T4,typename T5> ostream& operator << (ostream& os, const tuple<T1,T2,T3,T4,T5>& t){os << get<0>(t)<<" "<<get<1>(t)<<" "<<get<2>(t)<<" "<<get<3>(t)<<" "<<get<4>(t);return os;}
template<typename T1,typename T2,typename T3,typename T4,typename T5,typename T6> ostream& operator << (ostream& os, const tuple<T1,T2,T3,T4,T5,T6>& t){os << get<0>(t)<<" "<<get<1>(t)<<" "<<get<2>(t)<<" "<<get<3>(t)<<" "<<get<4>(t)<<" "<<get<5>(t);return os;}
template<typename T1,typename T2,typename T3,typename T4,typename T5,typename T6,typename T7> ostream& operator << (ostream& os, const tuple<T1,T2,T3,T4,T5,T6,T7>& t){os << get<0>(t)<<" "<<get<1>(t)<<" "<<get<2>(t)<<" "<<get<3>(t)<<" "<<get<4>(t)<<" "<<get<5>(t)<<" "<<get<6>(t);return os;}

//input
char tmp[1000];
#define nextInt(n) scanf("%d",&n)
#define nextLong(n) scanf("%lld",&n) //I64d
#define nextDouble(n) scanf("%lf",&n) 
#define nextChar(n) scanf("%c",&n)
#define nextString(n) scanf("%s",tmp);n=tmp

// values
template<typename T> T INF(){assert(false);};
template<> int INF<int>(){return 1<<28;};
template<> ll INF<ll>(){return 1LL<<58;};
template<> double INF<double>(){return 1e16;};

template<class T> T EPS(){assert(false);};
template<> int EPS<int>(){return 1;};
template<> ll EPS<ll>(){return 1LL;};
template<> double EPS<double>(){return 1e-8;};
template<> long double EPS<long double>(){return 1e-8;};

template<typename T,typename U> T pfmod(T v,U M){return fmod(fmod(v,M)+M,M);}

ll gcd_positive(ll a,ll b) { return b == 0 ? a : gcd_positive(b,a%b); }
ll gcd(ll a,ll b) { return gcd_positive(abs(a), abs(b)); }
ll lcm(ll a,ll b){return a/gcd(a,b)*b;}

namespace EGraph{
	typedef ll Cost;Cost CINF=INF<Cost>();
	struct Edge{
		int from,to;Cost cost;
		Edge(int from,int to,Cost cost)
		: from(from),to(to),cost(cost) {};
		bool operator<(Edge r) const{ return cost<r.cost;}
		bool operator>(Edge r) const{ return cost>r.cost;}
	};
	typedef vector<vector<Edge> >  Graph;
}
using namespace EGraph;


int dx[4]={1,0,-1,0},dy[4]={0,1,0,-1};

class subset{
private:
	struct Iter{
		int v,bit;vector<int> bs;
		int operator*(){
			int res=0,vi=0;
			REP(i,bs.size()){
				if(v&(1<<vi))res+=1<<bs[i];
				vi++;
			}
			return res;
		}
		bool operator!=(Iter& itr) {return v < itr.v;}
		void operator++(){++v;}
	};
	Iter i, n;
public:
	subset(int bit){
		int btmp=bit;
		vector<int> bs;
		int bc=0,d=0;
		while(btmp!=0){
			if(btmp%2){
				bc++;bs.push_back(d);
			}
			btmp/=2;d++;
		}
		i={0,bit,bs};n={1<<bc,bit,bs};
	}
	Iter& begin() {return i;}
	Iter& end() {return n;}
};

class Main{
	typedef ll Cost;

	Cost minimum_steiner_tree(const vector<int>& ts, const vector<vector<Cost>> &g) {
		const int n = g.size();
		if (ts.size() <= 1) return 0;

		// all-pair shortest
		vector<vector<Cost>> ds=g;REP(k,n)REP(i,n)REP(j,n) ds[i][j] = min(ds[i][j], ds[i][k] + ds[k][j]);

		vector<vector<Cost>> dp(1<<ts.size(),vector<ll>(n,INF<Cost>()));
		REP(i,ts.size())REP(q,n) dp[1 << i][q] = ds[ts[i]][q];
		
		REP(S,1<<ts.size()){
			REP(p,n)for(int E :subset(S)) dp[S][p]=min(dp[S][p],dp[E][p] + dp[S-E][p]);
			REP(p,n)REP(q,n) dp[S][p] = min(dp[S][p], dp[S][q] + ds[p][q] );
		}
		Cost res =INF<Cost>();REP(q,n)res = min(res,dp[((1 << ts.size())-1)][q]);
		return res;
	}

	public:
	void run(){
		while(true){
			int H,W;cin >> H >>W;if(H==0 && W==0)break;
			vector<vector<int>> board(H,vector<int>(W));
			REP(y,H)REP(x,W)cin >> board[y][x];

			vector<vector<ll>> mat(H*W,vector<ll>(H*W,INF<ll>()));
			REP(i,H*W)mat[i][i]=0;

			vector<int> vs;
			REP(y,H)REP(x,W)if(board[y][x])vs.push_back(y*W+x);
			
			REP(y,H)REP(x,W){
				REP(d,4){
					int ny=y+dy[d],nx=x+dx[d];
					if(!IN(0,nx,W) || !IN(0,ny,H))continue;
					mat[y*W+x][ny*W+nx]=1;
				}
			}
			cout << H*W - (1+minimum_steiner_tree(vs,mat)) <<endl;

		}
	}
};

int main(){
	cout <<fixed<<setprecision(20);
	cin.tie(0);
	ios::sync_with_stdio(false);
	Main().run();
	return 0;
}