Problem:
Score : 100 points

Problem Statement

You are parking at a parking lot. You can choose from the following two fee plans:

Plan 1: The fee will be A×T yen (the currency of Japan) when you park for T hours.

Plan 2: The fee will be B yen, regardless of the duration.

Find the minimum fee when you park for N hours.

Constraints

1≤N≤20

1≤A≤100

1≤B≤2000

All input values are integers.

Input

Input is given from Standard Input in the following format:

N A B

Output

When the minimum fee is x yen, print the value of x.

Sample Input 1

7 17 120

Sample Output 1

119

If you choose Plan 1, the fee will be 7×17=119 yen.

If you choose Plan 2, the fee will be 120 yen.

Thus, the minimum fee is 119 yen.

Sample Input 2

5 20 100

Sample Output 2

100

The fee might be the same in the two plans.

Sample Input 3

6 18 100

Sample Output 3

100

Solution in Ruby (2.3.3) (judge verdict: Runtime Error)

N,C=gets.chomp.split.map(&:to_i)
M = 200002
s = []
t = []
c = []
N.times do
    ss,tt,cc = gets.chomp.split.map(&:to_i)    
    s << ss
    t << tt
    c << cc
end

u = Array.new(M)
z = Array.new(M,0)
ans = 0
1.upto(C) do |i|
    0.upto(M-1) {|j| u[j] = 0}
    0.upto(N-1) do |j|
        if c[j] == i
            u[s[j]*2 - 1] += 1
            u[t[j]*2 + 1] -= 1
        end
    end
    1.upto(M-1) do |j|
         u[j] += u[j-1]
         if u[j] > 0
            z[j] += 1
         end
    end
end

puts z.max