zscoder wants to generate an input file for some programming competition problem.

His input is a string consisting of n letters 'a'. He is too lazy to write a generator so he will manually generate the input in a text editor.

Initially, the text editor is empty. It takes him x seconds to insert or delete a letter 'a' from the text file and y seconds to copy the contents of the entire text file, and duplicate it.

zscoder wants to find the minimum amount of time needed for him to create the input file of exactly n letters 'a'. Help him to determine the amount of time needed to generate the input.


-----Input-----

The only line contains three integers n, x and y (1 ≤ n ≤ 10^7, 1 ≤ x, y ≤ 10^9) — the number of letters 'a' in the input file and the parameters from the problem statement.


-----Output-----

Print the only integer t — the minimum amount of time needed to generate the input file.


-----Examples-----
Input
8 1 1

Output
4

Input
8 1 10

Output
8

Difficulty: interview

Starter code:

Solutions:
def recursion(n):
    if n == 1:
        return x
    if n == 2:
        return x + min(x , y)
    if n % 2 == 0:
        return recursion(n // 2) + min(y, x * (n - n//2))
    else:
        return min(recursion(n + 1), recursion(n - 1)) + x


import sys
sys.setrecursionlimit(10000000)
n, x, y = list(map(int, input().split()))
print(recursion(n))


import sys
sys.setrecursionlimit(100000)

from functools import lru_cache

@lru_cache()
def best(a):
    if a == 1:
        return x
    elif a > 0:
        if a == 2:
            return x + min(x, y)
        elif a % 2 == 0:

            return best(a//2) + min(y, (a - a//2) * x)
        else:
            return min(best(a-1) , best(a+1) ) + x



n, x, y = map(int, input().split())

print(best(n))

import sys
sys.setrecursionlimit(1000000)

def f(n):
    if n == 1:
        return x
    elif n == 2:
        return x + min(x, y)
    else:
        if n % 2 == 0:
            return f(n // 2) + min(y, x * (n - n // 2))
        else:
            return min(f(n + 1), f(n - 1)) + x

n, x, y = map(int, input().split())

print(f(n))

def main():
    def f(t):
        if t & 1:
            return x if t == 1 else min(f(t - 1), f(t + 1)) + x
        else:
            u = x * t
            return f(t // 2) + y if y * 2 < u else u

    n, x, y = list(map(int, input().split()))
    print(f(n))


def __starting_point():
    main()

__starting_point()

def main():
    def f(t):
        u = cache.get(t)
        if u is None:
            if t & 1:
                u = min(f(t - 1), f(t + 1)) + x
            else:
                u = x * t
                if y * 2 < u:
                    u = f(t // 2) + y
            cache[t] = u
        return u

    n, x, y = list(map(int, input().split()))
    cache = {1: x}
    print(f(n))


def __starting_point():
    main()

__starting_point()

n, a, b = input().split(' ')
n = int(n)
a = int(a)
b = int(b)
tk = tk2 = dk = dk2 = hg = hg2 = tag = tag2 = k1 = k2 = 0
kg = n
while kg >= 2:
    if kg % 2 != 0:
        tag = 1
        if tag == 1 and (kg-kg//2-1)*a < b:
            break
        hg2 = kg
        hg = (kg+1)//2
        while hg >= 2:
            if hg % 2 != 0:
                tag2 = 1
            if tag2 == 1 and (hg-hg//2-1)*a < b:
                break
            if tag2 == 0 and (hg-hg//2)*a < b:
                break
            if hg % 2 != 0:
                tk2 += 1
            hg //= 2
            tag2 = 0
            tk += 1
        t0 = b*tk + a*hg + a*tk2
        tag2 = 0
        hg = (hg2 - 1)//2
        while hg >= 2:
            if hg % 2 != 0:
                tag2 = 1
            if tag2 == 1 and (hg - hg//2 - 1) * a < b:
                break
            if tag2 == 0 and (hg - hg//2) * a < b:
                break
            if hg % 2 != 0:
                dk2 += 1
            hg //= 2
            tag2 = 0
            dk += 1
        t1 = b*dk + a*hg + a*dk2
        if t0 <= t1:
            kg += 1
        else:
            kg -= 1
        tk = tk2 = dk = dk2 = hg2 = 0
    if tag == 1:
        k2 += 1
    if (kg-kg//2)*a <= b:
        break
    kg //= 2
    tag = 0
    k1 += 1
t = b*k1 + k2*a + kg*a
print(t)


def fi(n):
    if n == 1:
        return x
    elif n == 2:
        return x + min(x, y)
    else:
        if n % 2 == 1:
            return min(fi(n-1), fi(n+1)) + x
        else:
            return fi(n//2) + min(y, x * (n//2))
        
n,x,y = map(int, input().split())
print(fi(n))

__author__ = 'Think'
n, x, y=[int(i) for i in input().split()]
def worth(num):
	if num%2==0:
		dub=y
		alt=x*(num//2)
	else:
		dub=y+x
		alt=x*((num//2)+1)
	return dub<alt, dub, alt

time=0
while n>0:
	parity=n%2
	should_double, dub, alt=worth(n)
	if should_double:
		time+=dub
		if parity==0:
			# print("Doubled, even,", n, n//2, time)
			n=n//2
			continue
		else:
			half=n//2
			if half%2==0:
				# print("Doubled, 1 mod 4,", n, half, time)
				n=half
				continue
			else:
				if ((half//2+1)*x+y)<half*x:
					# print("Doubled, 3 mod 4, continued", n, half+1, time)
					n=half+1
					continue
				else:
					# print("Doubled, 3 mod 4, end", n, half, time)
					time+=half*x
					break
	else:
		# print("Haven't doubled, ", n, time)
		time+=n*x
		break

print(time)






#import sys
#sys.stdin = open('in', 'r')
#n = int(input())
#a = [int(x) for x in input().split()]

n,x,y = list(map(int, input().split()))
import heapq
h = []
d = {}
heapq.heappush(h, (0, n))


r = -1
while r == -1:
    xh,nh = heapq.heappop(h)
    if nh not in d:
        d[nh] = xh
        if nh == 1:
            r = xh + x
        elif nh * x < y:
            r = xh + nh*x
        else:
            if (nh - 1) not in d:
                heapq.heappush(h, (xh + x, nh - 1))
            if nh & 1 == 0 and (nh // 2) not in d and y < (nh//2)*x:
                heapq.heappush(h, (xh + y, nh // 2))
            if (nh + 1) not in d:
                heapq.heappush(h, (xh + x, nh + 1))
            
            

print(r)


import sys
sys.setrecursionlimit(1000000)

def f(dp,x,y,n):
    if dp[n]!=-1:
        return dp[n]   
    if n%2==1:
        ans=x+min(f(dp,x,y,n-1) ,f(dp,x,y,n+1))
    else:
        ans=f(dp,x,y,n//2)+min(y,x*n//2)
    dp[n]=ans
    return ans

n,x,y=list(map(int,input().split()))
dp=[-1 for i in range(n+10)]
dp[1]=x
print(f(dp,x,y,n))