A. Water Buying

题目链接http://codeforces.com/problemset/problem/1118/A

time limit per test:1 second

memory limit per test:256 megabytes

Polycarp wants to cook a soup. To do it, he needs to buy exactly n liters of water.
There are only two types of water bottles in the nearby shop — 1-liter bottles and 2-liter bottles. There are infinitely many bottles of these two types in the shop.

The bottle of the first type costs a burles and the bottle of the second type costs b burles correspondingly.

Polycarp wants to spend as few money as possible. Your task is to find the minimum amount of money (in burles) Polycarp needs to buy exactly n liters of water in the nearby shop if the bottle of the first type costs a burles and the bottle of the second type costs b burles.
Input

The first line of the input contains one integer q(1<=q<=500)— the number of queries.

The next n lines contain queries. The i-th query is given as three space-separated integers n_i, a_i,b_i(1<=n_i<=10¹²,1<=a_i,b_i<=1000)— how many liters Polycarp needs in the i-th query, the cost (in burles) of the bottle of the first type in the i-th query and the cost (in burles) of the bottle of the second type in the i-th query, respectively.

Output

Print q integers. The i-th integer should be equal to the minimum amount of money (in burles) Polycarp needs to buy exactly n_i liters of water in the nearby shop if the bottle of the first type costs a_i burles and the bottle of the second type costs b_iburles.

Example

Input

4
10 1 3
7 3 2
1 1000 1
1000000000000 42 88

Output

10
9
1000
42000000000000

题目大意：你需要买N升的水，现有a类a元/1升，b类b元/升。问恰好装满N需要的最少钱。
emmm。。。刚开始我还以为是01背包，但10¹²让我放弃了原来的想法。
想一想，这里只有两个数据，我们又想到所有大于0的数都可以由n个2和1个1构成。那么我们的思路一下子就出来了。比较一下a的单价和b的单价如果a的单价小，我们就直接返回答案N*a。否则我们需要的钱就是(n/2)*b+a;
以下是详细代码：

#include <cstdio>
#define ll long long
int main()
{ll t,n,a,b;scanf ("%lld",&t);while (t--){scanf ("%lld%lld%lld",&n,&a,&b);double x=b/2;long long mon;if (x+1e-10<(double)a) {if (n&1) mon=(n/2)*b+a;else mon=(n/2)*b;}else mon=n*a;printf ("%lld\n",mon);}return 0;
}

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Codeforces Round #540 (Div. 3)--A. Water Buying(简单思维题-有点坑）

A. Water Buying

Input

Output

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