Problem:
 Score : 600 points    Problem Statement The squirrel Chokudai has N acorns.
One day, he decides to do some trades in multiple precious metal exchanges to make more acorns.  His plan is as follows:   Get out of the nest with N acorns in his hands.  Go to Exchange A and do some trades.  Go to Exchange B and do some trades.  Go to Exchange A and do some trades.  Go back to the nest.   In Exchange X  (X = A, B) , he can perform the following operations any integer number of times (possibly zero) in any order:   Lose g_{X} acorns and gain 1 gram of gold.  Gain g_{X} acorns and lose 1 gram of gold.  Lose s_{X} acorns and gain 1 gram of silver.  Gain s_{X} acorns and lose 1 gram of silver.  Lose b_{X} acorns and gain 1 gram of bronze.  Gain b_{X} acorns and lose 1 gram of bronze.   Naturally, he cannot perform an operation that would leave him with a negative amount of acorns, gold, silver, or bronze.  What is the maximum number of acorns that he can bring to the nest?
Note that gold, silver, or bronze brought to the nest would be worthless because he is just a squirrel.      Constraints  1 \leq N \leq 5000  1 \leq g_{X} \leq 5000  1 \leq s_{X} \leq 5000  1 \leq b_{X} \leq 5000  All values in input are integers.         Input Input is given from Standard Input in the following format:  N  g_A  s_A  b_A  g_B  s_B  b_B       Output Print the maximum number of acorns that Chokudai can bring to the nest.        Sample Input 1 23
1 1 1
2 1 1      Sample Output 1 46  He can bring 46 acorns to the nest, as follows:   In Exchange A , trade 23 acorns for 23 grams of gold. {acorns, gold, silver, bronze}={ 0,23,0,0 }  In Exchange B , trade 23 grams of gold for 46 acorns. {acorns, gold, silver, bronze}={ 46,0,0,0 }  In Exchange A , trade nothing. {acorns, gold, silver, bronze}={ 46,0,0,0 }   He cannot have 47 or more acorns, so the answer is 46 .

Solution (Python):
import sys
input = sys.stdin.readline

def F(N,A,B):
    AB = list(zip(A,B))
    AB = [(a,b) for a,b in AB if a < b] 
    AB.sort(key = lambda x: x[1]/x[0], reverse = True)
    if len(AB) == 0:
        return N
    if len(AB) == 1:
        a,b = AB[0]
        x = N//a
        return N + (b-a) * x
    if len(AB) == 2:
        (a,b),(c,d) = AB
        
        return max(N + (N - i * c) // a * (b-a) + i * (d-c) for i in range(a))
    
    dp = [0] * (N+1)
    for n in range(N+1):
        x = n
        for a,b in AB:
            if n >= a:
                y = dp[n-a] + b
                if x < y:
                    x = y
        dp[n] = x
    return dp[N]

N = int(input())
A = [int(x) for x in input().split()]
B = [int(x) for x in input().split()]

answer = F(F(N,A,B),B,A)
print(answer)


AB = [(1,2),(3,4)]
(a,b),(c,d) = AB

Solution (Python):
import sys
input = sys.stdin.readline

def F(N,A,B):
    
    
    AB = [(x,y) for x,y in zip(A,B) if x < y]
    dp = [0] * (N+1)
    for n in range(N+1):
        x = n
        for a,b in AB:
            if n >= a:
                y = dp[n-a] + b
                if x < y:
                    x = y
        dp[n] = x
    return dp[N]

N = int(input())
A = [int(x) for x in input().split()]
B = [int(x) for x in input().split()]

answer = F(F(N,A,B),B,A)
print(answer)

Solution (Python):
N = int(input())
CA = list(map(int, input().split()))
CB = list(map(int, input().split()))

def solve(n, w, v):
    dp = [0]*(n+1)
    for i in range(n):
        dp[i+1] = max(1+dp[i], dp[i+1])
        if i + w[0] < n+1:
            dp[i+w[0]] = max(dp[i] + v[0], dp[i+w[0]])
        if i + w[1] < n+1:
            dp[i+w[1]] = max(dp[i] + v[1], dp[i+w[1]])
        if i + w[2] < n+1:
            dp[i+w[2]] = max(dp[i] + v[2], dp[i+w[2]])
    return dp[-1]
print(solve(solve(N, CA, CB), CB, CA))

Solution (Python):
def solve(n,a,b):
    dp=[0]*(n+1)
    for w in range(n+1): dp[w]=max(w,dp[w-a[0]]+b[0]if w-a[0]>=0 else w,dp[w-a[1]]+b[1]if w-a[1]>=0 else w,dp[w-a[2]]+b[2]if w-a[2]>=0 else w)
    return dp[-1]
N,A,B=int(input()),list(map(int, input().split())),list(map(int, input().split()))
print(solve(solve(N,A,B),B,A))

Solution (Python):
import sys

def trade(n, a, b):
    a0, a1, a2 = a
    b0, b1, b2 = b
    dp = [0] * (n+1)
    for i in range(1, n+1):
        gold, silver, copper = 0, 0, 0
        if i >= a0:
            gold = dp[i-a0] + b0
        if i >= a1:
            silver = dp[i-a1] + b1
        if i >= a2:
            copper = dp[i-a2] + b2
        dp[i] = max(i, gold, silver, copper)

    return dp[n]


def main():
    input = sys.stdin.readline
    N = int(input())
    A = list(map(int, input().split()))
    B = list(map(int, input().split()))

    
    M = trade(N, A, B)
    
    return trade(M, B, A)


if __name__ == '__main__':
    print(main())

Solution (Python):
import sys

def main():
    input = sys.stdin.readline
    N = int(input())
    A = list(map(int, input().split()))
    B = list(map(int, input().split()))

    dp = [0] * (N+1)
    for i in range(1, N+1):
        gold, silver, copper = 0, 0, 0
        if i >= A[0]:
            gold = dp[i-A[0]] + B[0]
        if i >= A[1]:
            silver = dp[i-A[1]] + B[1]
        if i >= A[2]:
            copper = dp[i-A[2]] + B[2]
        dp[i] = max(i, gold, silver, copper)

    M = dp[N]
    dp = [0] * (M+1)
    for i in range(1, M+1):
        gold, silver, copper = 0, 0, 0
        if i >= B[0]:
            gold = dp[i-B[0]] + A[0]
        if i >= B[1]:
            silver = dp[i-B[1]] + A[1]
        if i >= B[2]:
            copper = dp[i-B[2]] + A[2]
        dp[i] = max(i, gold, silver, copper)

    return dp[M]


if __name__ == '__main__':
    print(main())

Solution (Python):


inpl = lambda: list(map(int,input().split()))
N = int(input())
rate = []
rate.append(inpl())
rate.append(inpl())
ABc = []
ABr = []
BAc = []
BAr = []
for i in range(3):
    rA, rB = rate[0][i], rate[1][i]
    if rB > rA:
        ABc.append(rA)
        ABr.append(rB)
    elif rA > rB:
        BAc.append(rB)
        BAr.append(rA)

dpAB = [0]*(N+1)
q = [0]*(len(ABc)+1)
for i in range(1,N+1):
    dpAB[i] = dpAB[i-1]+1
    for j in range(len(ABc)): 
        if i >= ABc[j]:
            dpAB[i] = max(dpAB[i], dpAB[i-ABc[j]] + ABr[j])

M = dpAB[N]
dpBA = [0]*(M+1)
q = [0]*(len(BAc)+1)
for i in range(1,M+1):
    k = 1
    dpBA[i] = dpBA[i-1]+1
    for j in range(len(BAc)):
        if i >= BAc[j]:
            dpBA[i] = max(dpBA[i], dpBA[i-BAc[j]] + BAr[j])

print(dpBA[M])

Solution (Python):
from fractions import gcd
inpl = lambda: list(map(int,input().split()))
def lcm(a,b):
    return a*b//gcd(a,b)

N = int(input())
rate = []
rate.append(inpl())
rate.append(inpl())
AB = []
BA = []
for i in range(3):
    rA, rB = rate[0][i], rate[1][i]
    if rB > rA:
        AB.append((rA, rB))
    elif rA > rB:
        BA.append((rB, rA))
for l in [AB, BA]:
    l.sort(key=lambda x: -x[1]/x[0])

def buy_and_sell(N, cost_ret):
    if len(cost_ret) == 0:
        return N
    else:
        minor_max = sum([ min([lcm(cost,cost_ret[i][0])-cost_ret[i][0] for cost,ret in cost_ret[:i]])
                          for i in range(1,len(cost_ret))])
        b0, s0 = cost_ret[0]
        n = max(0, N - minor_max) // b0
        Ndp = N - n*b0
        dp = [0]*(Ndp+1)
        w = [0]*(len(cost_ret)+1)
        for i in range(1,Ndp+1):
            k = 1
            for cost, ret in cost_ret:
                if i >= cost:
                    w[k] = dp[i-cost] + ret
                    k += 1
            dp[i] = max(dp[i-1]+1, max(w))
        return s0*n + dp[-1]

M = buy_and_sell(N, AB)
L = buy_and_sell(M, BA)
print(L)

Solution (Python):
from fractions import gcd
from functools import reduce
inpl = lambda: list(map(int,input().split()))
def lcm(a,b):
    return a*b//gcd(a,b)
def lcm_list(numbers):
    return reduce(lcm, numbers)

N = int(input())
rate = []
rate.append(inpl())
rate.append(inpl())
AB = []
BA = []
for i in range(3):
    rA, rB = rate[0][i], rate[1][i]
    if rB > rA:
        AB.append((rA, rB))
    elif rA > rB:
        BA.append((rB, rA))
for l in [AB, BA]:
    l.sort(key=lambda x: -x[1]/x[0])

def buy_and_sell(N, cost_ret):
    if len(cost_ret) == 0:
        return N
    else:
        Nunit = lcm_list([ x[0] for x in cost_ret ])
        b0, s0 = cost_ret[0]
        q = N // b0
        n = max(0, q - (len(cost_ret)-1)*Nunit//b0)
        Ndp = N - n*b0
        dp = [0]*(Ndp+1)
        w = [0]*(len(cost_ret)+1)
        for i in range(1,Ndp+1):
            k = 1
            for cost, ret in cost_ret:
                if i >= cost:
                    w[k] = dp[i-cost] + ret
                    k += 1
            dp[i] = max(dp[i-1]+1, max(w))
        return s0*n + dp[-1]

M = buy_and_sell(N, AB)
L = buy_and_sell(M, BA)
print(L)

Solution (Python):
from fractions import gcd
from functools import reduce
inpl = lambda: list(map(int,input().split()))
def lcm(a,b):
    return a*b//gcd(a,b)
def lcm_list(numbers):
    return reduce(lcm, numbers)

N = int(input())
rate = []
rate.append(inpl())
rate.append(inpl())
AB = []
BA = []
for i in range(3):
    rA, rB = rate[0][i], rate[1][i]
    if rB > rA:
        AB.append((rA, rB))
    elif rA > rB:
        BA.append((rB, rA))
for l in [AB, BA]:
    l.sort(key=lambda x: -x[1]/x[0])

def buy_and_sell(N, cost_ret):
    if len(cost_ret) == 0:
        return N
    else:
        Nunit = lcm_list([ x[0] for x in cost_ret ])
        b0, s0 = cost_ret[0]
        q = N // b0
        n = max(0, q - 2*Nunit//b0 + 1)
        Ndp = N - n*b0
        dp = [0]*(Ndp+1)
        w = [0]*(len(cost_ret)+1)
        for i in range(1,Ndp+1):
            k = 1
            for cost, ret in cost_ret:
                if i >= cost:
                    w[k] = dp[i-cost] + ret
                    k += 1
            dp[i] = max(dp[i-1]+1, max(w))
        return s0*n + dp[-1]

M = buy_and_sell(N, AB)
L = buy_and_sell(M, BA)
print(L)

Solution (Python):


import itertools
from collections import Counter
from collections import defaultdict
import bisect
from heapq import heappush, heappop


def main():
    N = int(input())
    ga, sa, ba = map(int, input().split())
    gb, sb, bb = map(int, input().split())

    
    

    dp1 = [0] * (N + 1)

    
    for i in range(1, N + 1):
        dp1[i] = max(dp1[i - 1] + 1,
                     (dp1[i - ga] + gb) if i - ga >= 0 else 0,
                     (dp1[i - sa] + sb) if i - sa >= 0 else 0,
                     (dp1[i - ba] + bb) if i - ba >= 0 else 0)
        

    N2 = dp1[N]
    dp2 = [0] * (N2 + 1)

    
    for i in range(1, N2 + 1):
        dp2[i] = max(dp2[i - 1] + 1,
                     (dp2[i - gb] + ga) if i - gb >= 0 else 0,
                     (dp2[i - sb] + sa) if i - sb >= 0 else 0,
                     (dp2[i - bb] + ba) if i - bb >= 0 else 0)
        

    print(dp2[N2])


if __name__ == '__main__':
    main()

Solution (Python):
import sys

sys.setrecursionlimit(10 ** 6)

def don(dk, rate, amin):
    if not rate:
        return dk
    if len(rate)==1:
        a,b=rate[0]
        p,m=divmod(dk,a)
        return p*b+m
    if len(rate)==2:
        a0,b0=rate[0]
        a1,b1=rate[1]
        if b0/a0<b1/a1:
            a0,b0,a1,b1=a1,b1,a0,b0
        p0,m=divmod(dk,a0)
        re=b0*p0
        p1,m=divmod(m,a1)
        re+=b1*p1+m
        while p0>0 and m>0:
            p0-=1
            m+=a0
            p2,m=divmod(m,a1)
            p1+=p2
            tmp=p0*b0+p1*b1+m
            if tmp>re:
                re=tmp
        return re
    if dk < amin:
        return dk
    if dp[dk] != -1:
        return dp[dk]
    mx = 0
    for a, b in rate:
        if a > dk: continue
        tmp = don(dk - a, rate, amin) + b
        if tmp > mx:
            mx = tmp
    dp[dk] = mx
    return mx

n = int(input())
aa = list(map(int, input().split()))
bb = list(map(int, input().split()))
atob = []
btoa = []
amin = 10 ** 7
bmin = 10 ** 7
for a, b in zip(aa, bb):
    if a < b:
        atob.append([a, b])
        if a < amin:
            amin = a
    elif a > b:
        btoa.append([b, a])
        if b < bmin:
            bmin = b
dp = [-1] * (n + 1)
n = don(n, atob, amin)
dp = [-1] * (n + 1)
print(don(n, btoa, bmin))

Solution (Python):
N=int(input())
rate=[list(map(int,input().split())) for i in range(2)]

def solve(d,r):
    l=len(r)
    if l==1:
        d=d//r[0][0]*r[0][1]+d%r[0][0]
    elif l==2:
        a=0
        w=[r[0][0],r[1][0]]
        v=[r[0][1]-r[0][0],r[1][1]-r[1][0]]
        for i in range(d//w[0]+1):
            a=max(a,v[0]*i+v[1]*((d-w[0]*i)//w[1]))
        d+=a
    elif l==3:
        a=[0]*(N+1)
        w=[r[0][0],r[1][0],r[2][0]]
        v=[r[0][1]-r[0][0],r[1][1]-r[1][0],r[2][1]-r[2][0]]
        for i in range(N+1):
            for j in range(l):
                if i>=w[j]:
                    a[i]=max(a[i],a[i-w[j]]+v[j])
        d+=a[-1]
    return d
r=[]
for i in range(3):
    if rate[0][i]<rate[1][i]:
        r.append((rate[0][i],rate[1][i]))
d=solve(N,r)
r=[]
for i in range(3):
    if rate[0][i]>rate[1][i]:
        r.append((rate[1][i],rate[0][i]))
d=solve(d,r)
print(d)

Solution (Python):
import math
import sys

N = int(input())
GA, SA, BA = list(map(int, input().split()))
GB, SB, BB = list(map(int, input().split()))

def knapsack(n, ga, sa, ba, gb, sb, bb):
    values = []
    weights = []
    if gb / ga > 1:
        values.append(gb - ga)
        weights.append(ga)
    if sb / sa > 1:
        values.append(sb - sa)
        weights.append(sa)
    if bb / ba > 1:
        values.append(bb - ba)
        weights.append(ba)
    if len(values) == 3:
        
        dp = [0] * (n + 1)
        dp[0] = n
        for i in range(1, n + 1):
            x = dp[i - 1]
            for w, v in zip(weights, values):
                if i - w >= 0:
                    x = max(x, dp[i - w] + v)
            dp[i] = x
        return dp[n]
    if len(values) == 2:
        w1, w2 = weights
        v1, v2 = values
        if (v1 + w1) / w1 < (v2 + w2) / w2:
            v1, v2 = v2, v1
            w1, w2 = w2, w1
        c1 = n // w1
        c2 = (n - w1 * c1) // w2
        ret = n + v1 * c1 + v2 * c2
        while c1 >= 0:
            a = n - w1 * c1 - w2 * c2
            c1 -= max(1, math.ceil((w2 - a) / w1))
            c2 = (n - w1 * c1) // w2
            ret = max(ret, n + v1 * c1 + v2 * c2)
            if w1 * c1 + w2 * c2 == n:
                break
        return ret
    if len(values) == 1:
        return n + n // weights[0] * values[0]
    return n

ans = knapsack(N, GA, SA, BA, GB, SB, BB)
ans = knapsack(ans, GB, SB, BB, GA, SA, BA)
print(int(ans))

Solution (Python):
import sys
sys.setrecursionlimit(10**7)
def LI(): return [int(x) for x in input().split()]
def II(): return int(input())
INTMIN = -9223372036854775808

N=II()
RA=LI()
RB=LI()
GAIN1=[]
GAIN2=[]
for i in range(3):
    if RA[i] < RB[i]:
        GAIN1.append((RA[i], RB[i]-RA[i]))
    if RA[i] > RB[i]:
        GAIN2.append((RB[i], RA[i]-RB[i]))

dp1 = [0]*(N+1)
for i in range(N+1):
    for cost, gain in GAIN1:
        if (i+cost) <= N:
            dp1[i+cost] = max(dp1[i+cost],dp1[i]+gain)

M = dp1[N]+N
dp2 = [0]*(M+1)
for i in range(M+1):
    for cost, gain in GAIN2:
        if (i+cost) <= M:
            dp2[i+cost] = max(dp2[i+cost],dp2[i]+gain)

print(M+dp2[M])

Solution (Python):
def exchange(n, s, d):
  v = [n] * (n + 1)
  r = [(1, 1)] + [(a, b) for a, b in zip(s, d) if a < b]

  for i in range(len(v) - 1):
    for a, b in r:
      if i + a < len(v):
        v[i + a] = max(v[i] - a + b, v[i + a])

  return v[-1]


def main():
  n = int(input())
  a = list(map(int, input().split()))
  b = list(map(int, input().split()))

  n = exchange(n, a, b)
  n = exchange(n, b, a)

  print(n)


if __name__ == '__main__':
  main()

Solution (Python):
import math
import os
import sys
 
if os.getenv("LOCAL"):
    sys.stdin = open("_in.txt", "r")
 
sys.setrecursionlimit(2147483647)
INF = float("inf")
 
N = int(sys.stdin.readline())
GA, SA, BA = list(map(int, sys.stdin.readline().split()))
GB, SB, BB = list(map(int, sys.stdin.readline().split()))
 
 
def knapsack(n, ga, sa, ba, gb, sb, bb):
    values = []
    weights = []
    if gb / ga > 1:
        values.append(gb - ga)
        weights.append(ga)
    if sb / sa > 1:
        values.append(sb - sa)
        weights.append(sa)
    if bb / ba > 1:
        values.append(bb - ba)
        weights.append(ba)
    if len(values) == 3:
        
        dp = [0] * (n + 1)
        dp[0] = n
        for i in range(1, n + 1):
            x = dp[i - 1]
            for w, v in zip(weights, values):
                if i - w >= 0:
                    x = max(x, dp[i - w] + v)
            dp[i] = x
        return dp[n]
    if len(values) == 2:
        w1, w2 = weights
        v1, v2 = values
        if (v1 + w1) / w1 < (v2 + w2) / w2:
            v1, v2 = v2, v1
            w1, w2 = w2, w1
        c1 = n // w1
        c2 = (n - w1 * c1) // w2
        ret = n + v1 * c1 + v2 * c2
        while c1 >= 0:
            a = n - w1 * c1 - w2 * c2
            c1 -= max(1, math.ceil((w2 - a) / w1))
            c2 = (n - w1 * c1) // w2
            ret = max(ret, n + v1 * c1 + v2 * c2)
            if w1 * c1 + w2 * c2 == n:
                break
        return ret
    if len(values) == 1:
        return n + n // weights[0] * values[0]
    return n
 
 
ans = knapsack(N, GA, SA, BA, GB, SB, BB)
ans = knapsack(ans, GB, SB, BB, GA, SA, BA)
print(int(ans))

Solution (Python):
import math
import os
import sys

if os.getenv("LOCAL"):
    sys.stdin = open("_in.txt", "r")

sys.setrecursionlimit(2147483647)
INF = float("inf")

N = int(sys.stdin.readline())
GA, SA, BA = list(map(int, sys.stdin.readline().split()))
GB, SB, BB = list(map(int, sys.stdin.readline().split()))


def knapsack(n, ga, sa, ba, gb, sb, bb):
    values = []
    weights = []
    if gb / ga > 1:
        values.append(gb - ga)
        weights.append(ga)
    if sb / sa > 1:
        values.append(sb - sa)
        weights.append(sa)
    if bb / ba > 1:
        values.append(bb - ba)
        weights.append(ba)
    if len(values) == 3:
        
        dp = [0] * (n + 1)
        dp[0] = n
        for i in range(1, n + 1):
            x = dp[i - 1]
            for w, v in zip(weights, values):
                if i - w >= 0:
                    x = max(x, dp[i - w] + v)
            dp[i] = x
        return dp[n]
    if len(values) == 2:
        w1, w2 = weights
        v1, v2 = values
        if (v1 + w1) / w1 < (v2 + w2) / w2:
            v1, v2 = v2, v1
            w1, w2 = w2, w1
        c1 = n // w1
        c2 = (n - w1 * c1) // w2
        ret = n + v1 * c1 + v2 * c2
        while c1 >= 0:
            a = n - w1 * c1 - w2 * c2
            c1 -= max(1, math.ceil((w2 - a) / w1))
            c2 = (n - w1 * c1) // w2
            ret = max(ret, n + v1 * c1 + v2 * c2)
            if w1 * c1 + w2 * c2 == n:
                break
        return ret
    if len(values) == 1:
        return n + n // weights[0] * values[0]
    return n


ans = knapsack(N, GA, SA, BA, GB, SB, BB)
ans = knapsack(ans, GB, SB, BB, GA, SA, BA)
print(int(ans))

Solution (Python):
import math
import os
import sys

if os.getenv("LOCAL"):
    sys.stdin = open("_in.txt", "r")

sys.setrecursionlimit(2147483647)
INF = float("inf")

N = int(sys.stdin.readline())
GA, SA, BA = list(map(int, sys.stdin.readline().split()))
GB, SB, BB = list(map(int, sys.stdin.readline().split()))


def knapsack(n, ga, sa, ba, gb, sb, bb):
    values = []
    weights = []
    if gb / ga > 1:
        values.append(gb - ga)
        weights.append(ga)
    if sb / sa > 1:
        values.append(sb - sa)
        weights.append(sa)
    if bb / ba > 1:
        values.append(bb - ba)
        weights.append(ba)
    if len(values) == 3:
        
        dp = [0] * (n + 1)
        dp[0] = n
        for i in range(1, n + 1):
            x = dp[i - 1]
            for w, v in zip(weights, values):
                if i - w >= 0:
                    x = max(x, dp[i - w] + v)
            dp[i] = x
        return dp[n]
    if len(values) == 2:
        w1, w2 = weights
        v1, v2 = values
        if (v1 + w1) / w1 < (v2 + w2) / w2:
            v1, v2 = v2, v1
            w1, w2 = w2, w1
        c1 = n // w1
        c2 = (n - w1 * c1) // w2
        ret = n + v1 * c1 + v2 * c2
        while c1 >= 0:
            a = n - w1 * c1 - w2 * c2
            c1 -= max(1, math.ceil((w2 - a) / w1))
            c2 = (n - w1 * c1) // w2
            ret = max(ret, n + v1 * c1 + v2 * c2)
            if w1 * c1 + w2 * c2 == n:
                break
        return ret
    if len(values) == 1:
        return n + n // weights[0] * values[0]
    return n


ans = knapsack(N, GA, SA, BA, GB, SB, BB)
ans = knapsack(ans, GB, SB, BB, GA, SA, BA)
print(int(ans))

Solution (Python):
import math
import os
import sys

if os.getenv("LOCAL"):
    sys.stdin = open("_in.txt", "r")

sys.setrecursionlimit(2147483647)
INF = float("inf")

N = int(sys.stdin.readline())
GA, SA, BA = list(map(int, sys.stdin.readline().split()))
GB, SB, BB = list(map(int, sys.stdin.readline().split()))

values = []
weights = []
if GB / GA > 1:
    values.append(GB - GA)
    weights.append(GA)
if SB / SA > 1:
    values.append(SB - SA)
    weights.append(SA)
if BB / BA > 1:
    values.append(BB - BA)
    weights.append(BA)

dp = [0] * (N + 1)
dp[0] = N
if values:
    for i in range(1, N + 1):
        x = dp[i - 1]
        for w, v in zip(weights, values):
            if i - w >= 0:
                x = max(x, dp[i - w] + v)
        dp[i] = x
    N = dp[N]

values = []
weights = []
if GA / GB > 1:
    values.append(GA - GB)
    weights.append(GB)
if SA / SB > 1:
    values.append(SA - SB)
    weights.append(SB)
if BA / BB > 1:
    values.append(BA - BB)
    weights.append(BB)

dp = [0] * (N + 1)
dp[0] = N
if len(values) == 3:
    for i in range(1, N + 1):
        x = dp[i - 1]
        for w, v in zip(weights, values):
            if i - w >= 0:
                x = max(x, dp[i - w] + v)
        dp[i] = x
    N = dp[N]
if len(values) == 2:
    w1, w2 = weights
    v1, v2 = values
    if (v1 + w1) / w1 < (v2 + w2) / w2:
        v1, v2 = v2, v1
        w1, w2 = w2, w1
    c1 = N // w1
    c2 = (N - w1 * c1) // w2
    ret = N + v1 * c1 + v2 * c2
    while c1 >= 0:
        a = N - w1 * c1 - w2 * c2
        c1 -= max(1, math.ceil((w2 - a) / w1))
        c2 = (N - w1 * c1) // w2
        ret = max(ret, N + v1 * c1 + v2 * c2)
        if w1 * c1 + w2 * c2 == N:
            break
    N = ret
if len(values) == 1:
    N += N // weights[0] * values[0]
print(int(N))

Solution (Python):
n = int(input())
aa = list(map(int, input().split()))
bb = list(map(int, input().split()))

rates_list = [[],[]]
for i in range(3):
	if aa[i] > bb[i]:
		rates_list[1].append([bb[i], aa[i]])
	else:
		rates_list[0].append([aa[i], bb[i]])

max_d = n
for j in range(2):
	rates = rates_list[j]
	if len(rates) == 1:
		max_d = (max_d // rates[0][0]) * rates[0][1] + max_d % rates[0][0]
	elif len(rates) == 2:
		val = [rates[0][1] * i for i in range(max_d // rates[0][0] + 1)]
		rest = [max_d - rates[0][0] * i for i in range(max_d // rates[0][0] + 1)]
		val = [val[i] + rates[1][1] * (rest[i] // rates[1][0]) + (rest[i] % rates[1][0]) if rest[i] > 0 else val[i] for i in range(len(val))]
		max_d = max(val)
	elif len(rates) == 3:
		dp = [(d // rates[0][0]) * rates[0][1] + d % rates[0][0] for d in range(max_d + 1)]
		for d in range(1, max_d + 1):
			dp[d] = max([dp[d]] + [dp[d - rates[i][0]] + rates[i][1] if d - rates[i][0] >= 0 else d for i in range(1, len(rates))])
		max_d = dp[-1]
print (max_d)

Solution (Python):
import sys
stdin = sys.stdin

sys.setrecursionlimit(10 ** 7)

def li(): return map(int, stdin.readline().split())
def li_(): return map(lambda x: int(x) - 1, stdin.readline().split())
def lf(): return map(float, stdin.readline().split())
def ls(): return stdin.readline().split()
def ns(): return stdin.readline().rstrip()
def lc(): return list(ns())
def ni(): return int(stdin.readline())
def nf(): return float(stdin.readline())

n = ni()
ga, sa, ba = li()
gb, sb, bb = li()

vg1, vg2 = gb - ga, ga - gb
vs1, vs2 = sb - sa, sa - sb
vb1, vb2 = bb - ba, ba - bb

dp1 = [0]*(n+1)

for i in range(1,n+1):
    dp1[i] = max(dp1[i-1]+1,
                  dp1[i-ga] + gb if i-ga >= 0 else 0,
                  dp1[i-sa] + sb if i-sa >= 0 else 0,
                  dp1[i-ba] + bb if i-ba >= 0 else 0)

m = max(n, dp1[n])
dp2 = [0] * (m+1)

for i in range(1, m+1):
    dp2[i] = max(dp2[i-1]+1,
                 dp2[i-gb] + ga if i-gb >= 0 else 0,
                 dp2[i-sb] + sa if i-sb >= 0 else 0,
                 dp2[i-bb] + ba if i-bb >= 0 else 0)

print(max(m, dp2[m]))

Solution (Python):
def f(a,b,N):

    tmpa,tmpb=[],[]
    for i in range(3):
        if a[i]<b[i]:
            tmpa.append(a[i])
            tmpb.append(b[i])
    a,b=tmpa,tmpb

    if len(a)==0: return N
    elif len(a)==1: return (N//a[0])*b[0]+N%a[0]

    elif len(a)==2:
        if a[0]<a[1]: a,b=a[::-1],b[::-1]

        i,ans=0,N
        while i*a[0]<=N:
            j=(N-i*a[0])//a[1]
            ans=max(ans,i*b[0]+j*b[1]+(N-i*a[0]-j*a[1]))
            i+=1
        return ans

    else:
        memo=[i for i in range(N+1)]

        for i in range(1,N+1):
            tmp=[]
            for j in range(len(a)):
                if i-a[j]>=0: tmp.append(memo[i-a[j]]+b[j])
            if tmp!=[]: memo[i]=max(tmp)
        return memo[N]

import sys
N=int(input())

A=list(map(int,input().split()))
B=list(map(int,input().split()))

N=f(A,B,N)
N=f(B,A,N)
print(N)

Solution (Python):
N = int(input())
A = list(map(int, input().split()))
B = list(map(int, input().split()))


ups = []
downs = []
eqs = []
for i in range(3):
    if A[i] < B[i]:
        ups.append((A[i], B[i]))
    elif A[i] == B[i]:
        eqs.append((A[i], B[i]))
    else:
        downs.append((A[i], B[i]))
ans = N

if len(eqs) == 3:
    print(N)
    exit()

if len(ups) == 0:
    tmp = A[:]
    A = B[:]
    B = tmp[:]
    ups = []
    downs = []
    eqs = []
    for i in range(3):
        if A[i] < B[i]:
            ups.append((A[i], B[i]))
        elif A[i] == B[i]:
            eqs.append((A[i], B[i]))
        else:
            downs.append((A[i], B[i]))

if len(ups) == 3:
    gold_diff = B[0]-A[0]
    silver_diff = B[1]-A[1]
    cupper_diff = B[2]-A[2]
    for gold in range(N//A[0]+1):
        left = N - gold*A[0]
        for silver in range(left//A[1]+1):
            cupper = (left - silver*A[1])//A[2]
            tmp_ans = (N
                       + gold*gold_diff
                       + silver*silver_diff
                       + cupper*cupper_diff)
            ans = max(ans, tmp_ans)
elif len(ups) == 2:
    gold_diff = ups[0][1]-ups[0][0]
    silver_diff = ups[1][1]-ups[1][0]
    for gold in range(N//ups[0][0]+1):
        left = N - gold*ups[0][0]
        silver = left // ups[1][0]
        tmp_ans = (N
                   + gold*gold_diff
                   + silver*silver_diff)
        ans = max(ans, tmp_ans)
    if len(downs) == 1:
        diff = downs[0][0]-downs[0][1]
        ans += (ans // downs[0][1]) * diff
elif len(ups) == 1:
    nowN = N + (N//ups[0][0])*(ups[0][1]-ups[0][0])
    if len(downs) == 2:
        gold_diff = downs[0][0]-downs[0][1]
        silver_diff = downs[1][0]-downs[1][1]
        for gold in range(nowN//downs[0][1]+1):
            left = nowN - gold*downs[0][1]
            silver = left // downs[1][1]
            tmp_ans = (nowN
                       + gold*gold_diff
                       + silver*silver_diff)
            ans = max(ans, tmp_ans)
    elif len(downs) == 1:
        ans = nowN + (nowN//downs[0][1])*(downs[0][0]-downs[0][1])
    else:
        ans = nowN
print(ans)

Solution (Python):


def small_dp(N,A,B):
    *X, = filter(lambda c: int.__sub__(*c)<0, zip(A,B))
    k = len(X)
    if k == 0:
        return N
    if k == 1:
        return X[0][1]*(N//X[0][0]) + N%X[0][0]
    if k == 2:
        c = 0
        for i in range(N//X[0][0]+1):
            j = (N-i*X[0][0])//X[1][0]
            c = max(X[0][1]*i + X[1][1]*j + (N-i*X[0][0])%X[1][0], c)
        return c
    if k == 3:
        if (N//X[1][0]+1)*(N//X[0][0]+1) <= 10**6 :
            return max(X[0][1]*i + max(X[1][1]*j + X[2][1]*((N-i*X[0][0]-j*X[1][0])//X[2][0]) + ((N-i*X[0][0]-j*X[1][0])%X[2][0]) for j in range((N-i*X[0][0])//X[1][0]+1)) for i in range(N//X[0][0]+1))
        else:
            dp = [0]*(N+1)
            for w in range(1,N+1):
                dp[w] = max(dp[w-X[i][0]]+X[i][1] if w>=X[i][0] else w for i in range(k))
            N = dp[-1]
            return N

def solve():
    N = int(input())
    A = list(map(int, input().split()))
    B = list(map(int, input().split()))
    res = small_dp(small_dp(N, A, B), B, A)

    return str(res)

if __name__ == '__main__':
    print(solve())

Solution (Python):

from itertools import product
from heapq import heappop, heappush

def small_dp(N,A,B):
    *X, = filter(lambda c: int.__sub__(*c)<0, zip(A,B))
    k = len(X)
    if k == 0:
        return N
    if k == 1:
        return X[0][1]*(N//X[0][0]) + N%X[0][0]
    if k == 2:
        c = 0
        for i in range(N//X[0][0]+1):
            j = (N-i*X[0][0])//X[1][0]
            c = max(X[0][1]*i + X[1][1]*j + (N-i*X[0][0])%X[1][0], c)
        return c
    if k == 3:
        if (N//X[1][0]+1)*(N//X[0][0]+1) <= 10**6 :
            return max(X[0][1]*i + max(X[1][1]*j + X[2][1]*((N-i*X[0][0]-j*X[1][0])//X[2][0]) + ((N-i*X[0][0]-j*X[1][0])%X[2][0]) for j in range((N-i*X[0][0])//X[1][0]+1)) for i in range(N//X[0][0]+1))
        else:
            import numpy as np
            dp = np.zeros(N+1, dtype=int)
            for w in range(1,N+1):
                dp[w] = max(dp[w-X[i][0]]+X[i][1] if w>=X[i][0] else w for i in range(k))
            N = dp[-1]
            return N

def solve():
    N = int(input())
    A = list(map(int, input().split()))
    B = list(map(int, input().split()))
    res = small_dp(small_dp(N, A, B), B, A)

    return str(res)

if __name__ == '__main__':
    print(solve())

Solution (Python):
N = int(input())
A = [int(i) for i in input().split()]
B = [int(i) for i in input().split()]

def knapzap(N, A, B) :
    dp = [0] * (N + 1)

    for n in range(1, N + 1) :
        dp[n] = max(
            dp[n-1] + 1,
            dp[n-A[0]] + B[0] if n - A[0] >= 0 else 0,
            dp[n-A[1]] + B[1] if n - A[1] >= 0 else 0,
            dp[n-A[2]] + B[2] if n - A[2] >= 0 else 0
        )

    return dp[N]

M = knapzap(N, A, B)
ret = knapzap(M, B, A)
print(ret)

Solution (Python):
import sys

readline = sys.stdin.readline

N = int(readline())

A = list(map(int, readline().split()))
B = list(map(int, readline().split()))


def nap(A, B, N):
    dp = [0] * (N + 1)

    
    
    for i in range(1, N + 1):
        dp[i] = max(
            dp[i - 1] + 1,
            dp[i - A[0]] + B[0] if i - A[0] >= 0 else -1,
            dp[i - A[1]] + B[1] if i - A[1] >= 0 else -1,
            dp[i - A[2]] + B[2] if i - A[2] >= 0 else -1
        )
    return dp[N]

A_to_B = nap(A, B, N)

B_to_A = nap(B, A, A_to_B)

print(B_to_A)