We have had record hot temperatures this summer. To avoid heat stroke, you decided to buy a quantity of drinking water at the nearby supermarket. Two types of bottled water, 1 and 0.5 liter, are on sale at respective prices there. You have a definite quantity in your mind, but are willing to buy a quantity larger than that if: no combination of these bottles meets the quantity, or, the total price becomes lower.

Given the prices for each bottle of water and the total quantity needed, make a program to seek the lowest price to buy greater than or equal to the quantity required.



Input

The input is given in the following format.


$A$ $B$ $X$


The first line provides the prices for a 1-liter bottle $A$ ($1\leq A \leq 1000$), 500-milliliter bottle $B$ ($1 \leq B \leq 1000$), and the total water quantity needed $X$ ($1 \leq X \leq 20000$). All these values are given as integers, and the quantity of water in milliliters.

Output

Output the total price.

Examples

Input

180 100 2400


Output

460


Input

200 90 2018


Output

450
#include <bits/stdc++.h>
#define all(v) v.begin(), v.end()
#define rall(v) v.rbegin(), v.rend()
#define rep(i,n) for (int i=0;i<(int)(n);i++)
#define codefor int test;scanf("%d",&test);while(test--)
#define INT(...) int __VA_ARGS__;in(__VA_ARGS__)
#define LL(...) ll __VA_ARGS__;in(__VA_ARGS__)
#define yn(ans) if(ans)printf("Yes\n");else printf("No\n")
#define YN(ans) if(ans)printf("YES\n");else printf("NO\n")
#define vector2d(type,name,h,...) vector<vector<type>>name(h,vector<type>(__VA_ARGS__))
#define umap unordered_map
#define uset unordered_set
using namespace std;
using ll = long long;
const int MOD=1000000007;
//入力系
void scan(int& a){scanf("%d",&a);}
void scan(long long& a){scanf("%lld",&a);}
template<class T> void scan(T& a){cin>>a;}
template<class T> void scan(vector<T>& vec){for(auto&& it:vec)scan(it);}
void in(){}
template <class Head, class... Tail> void in(Head& head, Tail&... tail){scan(head);in(tail...);}
//出力系
void print(const int& a){printf("%d",a);}
void print(const long long& a){printf("%lld",a);}
void print(const double& a){printf("%.15lf",a);}
template<class T> void print(const T& a){cout<<a;}
template<class T> void print(const vector<T>& vec){if(vec.empty())return;print(vec[0]);for(auto it=vec.begin();++it!= vec.end();){putchar(' ');print(*it);}}
void out(){putchar('\n');}
template<class T> void out(const T& t){print(t);putchar('\n');}
template <class Head, class... Tail> void out(const Head& head,const Tail&... tail){print(head);putchar(' ');out(tail...);}
//デバッグ系
template<class T> void dprint(const T& a){cerr<<a;}
template<class T> void dprint(const vector<T>& vec){if(vec.empty())return;cerr<<vec[0];for(auto it=vec.begin();++it!= vec.end();){cerr<<" "<<*it;}}
void debug(){cerr<<endl;}
template<class T> void debug(const T& t){dprint(t);cerr<<endl;}
template <class Head, class... Tail> void debug(const Head& head, const Tail&... tail){dprint(head);cerr<<" ";debug(tail...);}
ll intpow(ll a, ll b){ ll ans = 1; while(b){ if(b & 1) ans *= a; a *= a; b /= 2; } return ans; }
ll modpow(ll a, ll b, ll p){ ll ans = 1; while(b){ if(b & 1) (ans *= a) %= p; (a *= a) %= p; b /= 2; } return ans; }

//小数点以下を切り上げる割り算
int updivide(int a,int b){
    if(b==1) return a;
    else if(a%b==0) return a/b;
    else return (a/b)+1;
}

int main(){
    INT(a,b,x);
    int ans=0;
    if(a>=2*b){
        ans=b*updivide(x,500);
    }else if(a<=b){
        ans=a*updivide(x,1000);
    }else if(a<2*b&&a>b){
        ans=a*(x/1000);
        x%=1000;
        if(x>500)ans+=a;
        else if(x>0)ans+=b;
    }
    out(ans);
}

