Problem: Example

Input

2
10 10


Output

40.00000000

Solution (in CPP):

Solution:
#include <algorithm>
#include <cmath>
#include <climits>
#include <cstdio>
#include <cstdlib>
#include <cstring>
#include <fstream>
#include <iostream>
#include <list>
#include <map>
#include <queue>
#include <set>
#include <sstream>
#include <stack>
#include <string>
#include <vector>
#include <cassert>
#include <functional>

using namespace std;

#define LOG(...) printf(__VA_ARGS__)
//#define LOG(...)
#define FOR(i,a,b) for(int i=(int)(a);i<(int)(b);++i)
#define REP(i,n) for(int i=0;i<(int)(n);++i)
#define ALL(a) (a).begin(),(a).end()
#define RALL(a) (a).rbegin(),(a).rend()
#define EXIST(s,e) ((s).find(e)!=(s).end())
#define SORT(c) sort((c).begin(),(c).end())
#define RSORT(c) sort((c).rbegin(),(c).rend())
#define CLR(a) memset((a), 0 ,sizeof(a))

typedef long long ll;
typedef unsigned long long ull;
typedef vector<bool> vb;
typedef vector<int> vi;
typedef vector<ll> vll;
typedef vector<vb> vvb;
typedef vector<vi> vvi;
typedef vector<vll> vvll;
typedef pair<int, int> pii;
typedef pair<ll, ll> pll;

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

struct UnionFind {
	vector<int> v;
	UnionFind(int n) : v(n)  { for (int i = 0; i < n; i++) v[i] = i; }
	int  find(int x)         { return v[x] == x ? x : v[x] = find(v[x]); }
	void unite(int x, int y) { v[find(x)] = find(y); }
};

int main() {
	int n;
	cin >> n;
	vector<double> vd(n);
	vector<double> vx(n);
	REP(i, n)
		cin >> vd[i];
	vx = vd;
	
	REP(i,n) {
		for (int j = i-1;j >= 0;j--) {
			vx[i] = max(vx[i], vx[j]+sqrt((vd[i]+vd[j])*(vd[i] + vd[j])- (vd[i] - vd[j])*(vd[i] - vd[j])));
		}
	}
	double ans = 0.0;
	REP(i, n)
		ans = max(ans, vx[i] + vd[i]);
	printf("%.8lf\n", ans);
}