Three displays CodeForces - 987C （dp）

C. Three displays

time limit per test

1 second

memory limit per test

256 megabytes

input

standard input

output

standard output

It is the middle of 2018 and Maria Stepanovna, who lives outside Krasnokamensk (a town in Zabaikalsky region), wants to rent three displays to highlight an important problem.

There are $\mathrm{nn displays\; placed\; along\; a\; road,\; and\; the ii-th\; of\; them\; can\; display\; a\; text\; with\; font\; size sisi only.\; Maria\; Stepanovna\; wants\; to\; rent\; such\; three\; displays\; with\; indices i<j<ki<j<k that\; the\; font\; size\; increases\; if\; you\; move\; along\; the\; road\; in\; a\; particular\; direction.\; Namely,\; the\; condition si<sj<sksi<sj<sk should\; be\; held.}$

The rent cost is for the $\mathrm{ii-th\; display\; is cici.\; Please\; determine\; the\; smallest\; cost\; Maria\; Stepanovna\; should\; pay.}$

Input

The first line contains a single integer $\mathrm{nn (3\le n\le 30003\le n\le 3000) —\; the\; number\; of\; displays.}$

The second line contains $\mathrm{nn integers s1,s2,\dots ,sns1,s2,\dots ,sn (1\le si\le 1091\le si\le 109) —\; the\; font\; sizes\; on\; the\; displays\; in\; the\; order\; they\; stand\; along\; the\; road.}$

The third line contains $\mathrm{nn integers c1,c2,\dots ,cnc1,c2,\dots ,cn (1\le ci\le 1081\le ci\le 108) —\; the\; rent\; costs\; for\; each\; display.}$

Output

If there are no three displays that satisfy the criteria, print -1. Otherwise print a single integer — the minimum total rent cost of three displays with indices $\mathrm{i<j<ki<j<k such\; that si<sj<sksi<sj<sk.}$

Examples

input

5
2 4 5 4 10
40 30 20 10 40

output

90

input

3
100 101 100
2 4 5

output

-1

input

10
1 2 3 4 5 6 7 8 9 10
10 13 11 14 15 12 13 13 18 13

output

33

Note

In the first example you can, for example, choose displays $\mathrm{11, 44 and 55,\; because s1<s4<s5s1<s4<s5 (2<4<102<4<10),\; and\; the\; rent\; cost\; is 40+10+40=9040+10+40=90.}$

In the second example you can't select a valid triple of indices, so the answer is -1.

题意：拿三样物品，价值要和顺序都递增，cost总和最少

题解：dp，改一下板子就可以了

#include<cstdio>
#include<iostream>
#include<algorithm>
#include<cstring>
#include<sstream>
#include<cmath>
#include<cstdlib>
#include<queue>
#include<map>
#include<set>
using namespace std;
#define INF 0x3f3f3f3f
const int maxn=3005;

int main()
{
    int n;
    int ans=INF;
    int val[maxn],cost[maxn],f[maxn][4];
    cin>>n;
    for(int i=0;i<n;i++)
        cin>>val[i];
    for(int i=0;i<n;i++)
        cin>>cost[i];
    memset(f, INF, sizeof(f));
    for (int i = 0; i < n; i++)
    {
        f[i][0] = cost[i];
        for (int j = 0; j < i; j++)
            if (val[j] < val[i])
                f[i][1] =min(f[i][1], f[j][0] + cost[i]);
        for (int j = 0; j < i; j++)
            if (val[j] < val[i])
                f[i][2] =min(f[i][2], f[j][1] + cost[i]);
        
    }
    for(int i=0;i<n;i++)
        ans=min(ans,f[i][2]);
    if(ans!=INF)
        cout<<ans<<endl;
    else
        cout<<-1<<endl;
    
}