#include <bits/stdc++.h>
#define syosu(x) fixed<<setprecision(x)
using namespace std;
typedef long long ll;
typedef unsigned int uint;
typedef unsigned long long ull;
typedef pair<int,int> P;
typedef pair<double,double> pdd;
typedef pair<ll,ll> pll;
typedef vector<int> vi;
typedef vector<vi> vvi;
typedef vector<double> vd;
typedef vector<vd> vvd;
typedef vector<ll> vl;
typedef vector<vl> vvl;
typedef vector<string> vs;
typedef vector<P> vp;
typedef vector<vp> vvp;
typedef vector<pll> vpll;
typedef pair<int,P> pip;
typedef vector<pip> vip;
const int inf=1<<29;
const ll INF=1ll<<60;
const double pi=acos(-1);
const double eps=1e-11;
const ll mod=1e9+7;
const int dx[4]={-1,0,1,0},dy[4]={0,-1,0,1};

ll n,res=INF;
vi a;

void dfs(int I,vp b){
	if(I==n){
		ll x=0;
		for(auto p:b) x+=p.second;
		res=min(res,x);
		return;
	}
	b.push_back({1<<I,a[I]});
	dfs(I+1,b);
	b.pop_back();
	int m=b.size();
	for(int i=0;i<1<<m;i++){
		int t=0,cnt=0;
		for(int j=0;j<m;j++) if(i&1<<j){
			if(t&b[j].first){
				t=-1;
				break;
			}
			t|=b[j].first;
			cnt++;
		}
		if(t==-1||cnt>a[I]) continue;
		vp c;
		if(cnt<a[I]) c.push_back({1<<I,a[I]-cnt});
		for(int j=0;j<m;j++){
			if(i&1<<j){
				P p=b[j];
				if(p.second>1){
					c.push_back({p.first+(1<<I),1});
					c.push_back({p.first,p.second-1});
				}
				else c.push_back({p.first+(1<<I),p.second});
			}
			else c.push_back(b[j]);
		}
		dfs(I+1,c);
	}
}

int main(){
	cin>>n;
	a=vi(n);
	for(auto &i:a) cin>>i;
	dfs(0,vp());
	cout<<res<<endl;
}

### Prompt

Develop a solution in CPP to the problem described below:

There is a complete graph of m vertices. Initially, the edges of the complete graph are uncolored. Sunuke did the following for each i (1 ≤ i ≤ n): Select ai vertices from the complete graph and color all edges connecting the selected vertices with color i. None of the sides were painted in multiple colors. Find the minimum value that can be considered as m.

Constraints

* 1 ≤ n ≤ 5
* 2 ≤ ai ≤ 109

Input


n
a1
.. ..
an


Output

Output the minimum value of m on one line.

Examples

Input

2
3
3


Output

5


Input

5
2
3
4
5
6


Output

12

### Response

```cpp
#include <bits/stdc++.h>
#define syosu(x) fixed<<setprecision(x)
using namespace std;
typedef long long ll;
typedef unsigned int uint;
typedef unsigned long long ull;
typedef pair<int,int> P;
typedef pair<double,double> pdd;
typedef pair<ll,ll> pll;
typedef vector<int> vi;
typedef vector<vi> vvi;
typedef vector<double> vd;
typedef vector<vd> vvd;
typedef vector<ll> vl;
typedef vector<vl> vvl;
typedef vector<string> vs;
typedef vector<P> vp;
typedef vector<vp> vvp;
typedef vector<pll> vpll;
typedef pair<int,P> pip;
typedef vector<pip> vip;
const int inf=1<<29;
const ll INF=1ll<<60;
const double pi=acos(-1);
const double eps=1e-11;
const ll mod=1e9+7;
const int dx[4]={-1,0,1,0},dy[4]={0,-1,0,1};

ll n,res=INF;
vi a;

void dfs(int I,vp b){
	if(I==n){
		ll x=0;
		for(auto p:b) x+=p.second;
		res=min(res,x);
		return;
	}
	b.push_back({1<<I,a[I]});
	dfs(I+1,b);
	b.pop_back();
	int m=b.size();
	for(int i=0;i<1<<m;i++){
		int t=0,cnt=0;
		for(int j=0;j<m;j++) if(i&1<<j){
			if(t&b[j].first){
				t=-1;
				break;
			}
			t|=b[j].first;
			cnt++;
		}
		if(t==-1||cnt>a[I]) continue;
		vp c;
		if(cnt<a[I]) c.push_back({1<<I,a[I]-cnt});
		for(int j=0;j<m;j++){
			if(i&1<<j){
				P p=b[j];
				if(p.second>1){
					c.push_back({p.first+(1<<I),1});
					c.push_back({p.first,p.second-1});
				}
				else c.push_back({p.first+(1<<I),p.second});
			}
			else c.push_back(b[j]);
		}
		dfs(I+1,c);
	}
}

int main(){
	cin>>n;
	a=vi(n);
	for(auto &i:a) cin>>i;
	dfs(0,vp());
	cout<<res<<endl;
}

```