Problem:
Score : 100 points

Problem Statement

There are N flowers arranged in a row.
For each i (1 \leq i \leq N), the height and the beauty of the i-th flower from the left is h_i and a_i, respectively.
Here, h_1, h_2, \ldots, h_N are all distinct.

Taro is pulling out some flowers so that the following condition is met:

The heights of the remaining flowers are monotonically increasing from left to right.

Find the maximum possible sum of the beauties of the remaining flowers.

Constraints

All values in input are integers.

1 \leq N \leq 2 × 10^5

1 \leq h_i \leq N

h_1, h_2, \ldots, h_N are all distinct.

1 \leq a_i \leq 10^9

Input

Input is given from Standard Input in the following format:

N
h_1 h_2 \ldots h_N
a_1 a_2 \ldots a_N

Output

Print the maximum possible sum of the beauties of the remaining flowers.

Sample Input 1

4
3 1 4 2
10 20 30 40

Sample Output 1

60

We should keep the second and fourth flowers from the left.
Then, the heights would be 1, 2 from left to right, which is monotonically increasing, and the sum of the beauties would be 20 + 40 = 60.

Sample Input 2

1
1
10

Sample Output 2

10

The condition is met already at the beginning.

Sample Input 3

5
1 2 3 4 5
1000000000 1000000000 1000000000 1000000000 1000000000

Sample Output 3

5000000000

The answer may not fit into a 32-bit integer type.

Sample Input 4

9
4 2 5 8 3 6 1 7 9
6 8 8 4 6 3 5 7 5

Sample Output 4

31

We should keep the second, third, sixth, eighth and ninth flowers from the left.

Solution in C (GCC 9.2.1) (judge verdict: Runtime Error)

#pragma region kyopuro_templates
#pragma GCC optimize("Ofast")
#include<stdio.h>
#include<stdlib.h>
#include<math.h>
#include<string.h>
#include<stdbool.h>
#include<assert.h>
#include<time.h>
#include<ctype.h>
typedef long long ll;
typedef long double ld;
#define rep(i,l,r)for(ll i=(l);i<(r);i++)
#define repp(i,l,r,k)for(ll i=(l);i<(r);i+=(k))
#define rrep(i,l,r)for(ll i=(l);i>=(r);i--)
#define INF (1LL<<62)
#define MOD1 1000000007
#define MOD2 998244353
#define MAX_N (1 << 20)
#define YES printf("Yes\n")
#define NO printf("No\n")
#define PN printf("\n")
#define charsize 100005 //10^5+5
#define PI 3.141592653589793238

void swap(ll *a, ll *b){ll c;c=*b;*b=*a;*a= c;}
void cin(ll *n){ scanf("%lld",&(*n)); }
void PriAll1(ll a[], ll n){ rep(i,0,n){ printf("%lld",a[i]); if(i!=n-1) printf(" "); }PN; }
ll max2(ll a,ll b){return a>=b?a:b;}
ll min2(ll a,ll b){return a>=b?b:a;}
ll min3(ll a, ll b, ll c){return (a<=b && a<=c) ? a : b<=c ? b : c;}
ll max3(ll a, ll b, ll c){return (a>=b && a>=c) ? a : b>=c ? b : c;}
ll minn(ll n, ll a[]){ll b=INF;rep(i,0,n) b=min2(b,a[i]);return b;}
ll maxn(ll n, ll a[]){ll b=-INF;rep(i,0,n) b=max2(b,a[i]);return b;}
ll POW(ll a, ll b){ll c=1;rep(i,0,b) c*=a;return c;}
double POW_d(double a, double b){double c=1;rep(i,0,b) c*=a;return c;}
ll gcd(ll a,ll b){return b?gcd(b,a%b):a;}
ll lcm(ll a,ll b){return a/gcd(a,b)*b;}
ll mod_MOD1(ll n){n+= n<0?((-n)/MOD1+1)*MOD1:0; return n%=MOD1;}
ll mod_p(ll n ,ll p){n+= n<0?((-n)/p+1)*p:0; return n%=p;}
ll change_into_num(char s[] , ll len, ll p){ return !p ? 0 : POW(10,p-1)*(s[len-p]-'0') + change_into_num(s,len,p-1); }
ll digits(ll a, ll b){return a/b?1+digits(a/b,b):1;}
ll base(ll n, ll a, ll i){return i==1?n%a:base(n/a,a,i-1);}
ll is_inArr1(ll x, ll n){ return ( x<0 || x>=n ) ? 0 : 1 ; }
ll is_inArr2(ll y, ll x, ll h, ll w){ return ( y<0 || y>=h || x<0 || x>=w ) ? 0 : 1 ; }


void lr_lower( int *l, int *r, ll am, ll val , int type ){ (type<3) ? ( am < val ?  ( *l = (*l+*r)/2 ) : ( *r= (*l+*r)/2 ) ) : ( am <= val ? ( *l = (*l+*r)/2 ) : ( *r= (*l+*r)/2 ) ); }
void lr_upper( int *l, int *r, ll am, ll val , int type ){ (type<3) ? ( am <= val ?  ( *l = (*l+*r)/2 ) : ( *r= (*l+*r)/2 ) ) : ( am < val ? ( *l = (*l+*r)/2 ) : ( *r= (*l+*r)/2 ) ); }
int cmp_lower( ll a, ll b, int type ){ return (type==1) ? ( a==b ? 1 : 0 ) : (type==2) ? ( a>=b ? 1 : 0 ) : ( a>b ? 1 : 0 ) ; }
int cmp_upper( ll a, ll b, int type ){ return (type==1) ? ( a==b ? 1 : 0 ) : (type==2) ? ( a<=b ? 1 : 0 ) : ( a<b ? 1 : 0 ) ; }
// return smallest p  which meets  a[p]==val :1  >=:2   >:3
ll lower_bound( ll a[], int l, int r, ll val , int type ){  while(r-l>1) lr_lower(&l,&r,a[ (l+r)/2 ],val,type);  return cmp_lower(a[l],val,type) ? l : cmp_lower(a[r],val,type) ? r : -1;  }
// return biggest p  which meets   a[p]==val :1  <=:2   <:3
ll upper_bound( ll a[], int l, int r, ll val , int type ){  while(r-l>1) lr_upper(&l,&r,a[ (l+r)/2 ],val,type); return cmp_upper(a[r],val,type) ? r : cmp_upper(a[l],val,type) ? l : -1; }
// count i  which meets ai==x
ll count(ll a[], int l, int r, ll x){  int p = lower_bound(a,l,r,x,1);  return p==-1 ? 0 : upper_bound(a,p,r,x,1)-p+1; }

ll *factors[2] , fac_cnt=0 , is_factor_prepared=0;
ll factor_pre(){  rep(i,0,1){ if(is_factor_prepared++) return 0; }  ll tmp=(1e6)/2+1, fac_tmp[tmp];  rep(i,0,tmp){fac_tmp[i]=i?2*i+1:2;}  rep(i,1,tmp){if(fac_tmp[i]){  repp(j,3,tmp/(2*i+1)+1,2 ){  if( j*(2*i+1)<tmp ) fac_tmp[ (j*(2*i+1)-1)/2 ]=0;  }  }else continue;}  rep(i,0,tmp){if(fac_tmp[i]){  rep(j,0,2){ factors[j] = realloc( factors[j] , sizeof(ll)*( fac_cnt +1 ) );  factors[j][j?fac_cnt++:fac_cnt]=j?0:fac_tmp[i];  }  } }  return 0;  }
ll factor(ll n, ll new_common_plus){ factor_pre();  rep(i,0,fac_cnt){ ll cnt=0; rep(j,0,1){ while( ( cnt+= n %factors[0][i]==0 ? 1 : 0 )  && (n/=factors[0][i]) %factors[0][i]==0 ) continue; } factors[1][i]= new_common_plus==1 ? cnt :  new_common_plus==2 ? max2(factors[1][i],cnt) : factors[1][i]+cnt ;  if( factors[0][i]> n ) break; } return n; }
ll judge_prime(ll n){ factor_pre(); rep(i,0,fac_cnt){ if(n<factors[0][i]*factors[0][i] || n==factors[0][i]) break; else if(n%factors[0][i]==0) n/=n; }  return n==1?0:1; }

ll *mf_arr,*inv_arr,*finv_arr,is_minv_made=0,is_mf_made=0,num_of_inv=2*1e6+10;
ll makeinv(ll n , ll mod){  rep(i,0,1){if(is_minv_made++) return 0;}  inv_arr = realloc(inv_arr, sizeof(ll)*2 );  finv_arr = realloc(finv_arr, sizeof(ll)*2 );  inv_arr[1]=1;finv_arr[0]=finv_arr[1]=1;  rep(i,2,n+1){  inv_arr = realloc(inv_arr, sizeof(ll)*(i+1) );  finv_arr = realloc(finv_arr, sizeof(ll)*(i+1) );  inv_arr[i]= mod - inv_arr[mod%i] * (mod / i) % mod;  finv_arr[i] = finv_arr[i - 1] * inv_arr[i] % mod;  }  return 0; }
ll make_mf(ll n, ll mod){  rep(i,0,1){ if(is_mf_made++) return 0; }  mf_arr = realloc(mf_arr, sizeof(ll)*2 );  ll x=1;  mf_arr[0]=mf_arr[1]=x;  rep(i,2,n+1){   x=x*i%mod;  mf_arr = realloc(mf_arr, sizeof(ll)*(i+1) );  mf_arr[i]=x; }  return 0;  }
ll m_inv(ll x, ll mod, ll is_fac ){ makeinv(num_of_inv,mod);  return is_fac?finv_arr[x]:inv_arr[x]; }
ll m_f(ll x, ll mod){  make_mf(num_of_inv,mod);  return mf_arr[x];  }
ll mod_nck(ll n, ll k, ll mod){ return m_f(n,mod)*m_inv(k,mod,1)%mod*m_inv(n-k,mod,1)%mod; }
ll m_p(ll r,ll n,ll mod){  ll t=1,s=r;  while(n>0){ t = (n&1) ? t*s%mod : t;  s=s*s%mod; n>>=1; }  return r?t:0;  }
ll m_mul2(ll a, ll b, ll mod){ return a*b%mod; }
ll m_mul3(ll a, ll b, ll c, ll mod){ return m_mul2(a*b%mod,c,mod); }
ll m_mul4(ll a, ll b, ll c, ll d, ll mod){ return m_mul3(a*b%mod,c,d,mod); }
ll m_mul5(ll a, ll b, ll c, ll d, ll e, ll mod){ return m_mul4(a*b%mod,c,d,e,mod); }

int upll(const void*a, const void*b){return*(ll*)a<*(ll*)b?-1:*(ll*)a>*(ll*)b?1:0;}
int downll(const void*a, const void*b){return*(ll*)a<*(ll*)b?1:*(ll*)a>*(ll*)b?-1:0;}
int cmp_string( const void * a , const void * b ) {  return strcmp( (char *)a , (char *)b ); }  // qsort((void*)s,n,sizeof(s[0]),int_sort );
int cmp_char(const void * a, const void * b) { return *(char *)a - *(char *)b;}
void sortup(ll*a,int n){qsort(a,n,sizeof(ll),upll);}
void sortdown(ll*a,int n){qsort(a,n,sizeof(ll),downll);}
void sort_string(int n,int size,char s[][size]){ qsort( (void*)s , n , sizeof(s[0]) , cmp_string ); }
void sort_char(char *s){ qsort( (void *)s , strlen(s) , sizeof(char) , cmp_char ); }
ll unique_string(ll n ,ll size, char s[][size]){ ll ans=1; rep(i,1,n) if( strcmp(s[i],s[i-1]) ) ans++; return ans; }
ll unique_num(ll n , ll a[]){ ll ans=1; rep(i,1,n) if( a[i]!=a[i-1] ) ans++; return ans; }

ll compare(ll a, ll b){ return a<b?-1:a>b?1:0; }
typedef struct{ ll a , b;}fr;
int cmp1( const void *p, const void *q ){  
    ll pa=((fr*)p)->a; ll qa=((fr*)q)->a;  return compare(pa,qa);  
}
int cmp2( const void *p, const void *q ){
    ll pa=((fr*)p)->a; ll qa=((fr*)q)->a;  return compare(qa,pa);
}
void strsortup(fr*a,int n){qsort(a,n,sizeof(fr),cmp1);}
void strsortdown(fr*a,int n){qsort(a,n,sizeof(fr),cmp2);}

void sort_partial(ll a[],int begin,int end,int is_increase){
    ll *b;  b = (ll *) malloc( sizeof(ll)*(end-begin) );

    rep(i,begin,end) b[i-begin]=a[i];
    if(is_increase) sortup(b,end-begin); else sortdown(b,end-begin);
    rep(i,begin,end) a[i]=b[i-begin];
}


#pragma region AVL
/*---------------------------AVL start--------------------------------*/
//https://qiita.com/mikecat_mixc/items/e9f8248de2ae7f7a0a29
typedef struct node_AVL_set{  
    ll val;
    int diff;
    int cnt;
    struct node_AVL_set *child[2];
}AVL_set;
void AVL_set_inside_rotate(AVL_set **node, int is_right){
    int l = is_right==false , r = is_right==true , sign = is_right ? 1 : -1;
    if((*node)->child[l] != NULL){
        AVL_set* left = (*node)->child[l];
        int a= (*node)->diff * sign , b= left->diff * sign ,na,nb;
        if(b+1){
            na=a-1-b;
            nb= (a-b) ? b-1 : a-2;
        }else{
            na=a-1;
            nb= a ? b-1 : a+b-2;
        }
        (*node)->diff = na * sign;
        left->diff = nb * sign;
        /* rotate-> */
        (*node)->child[l] = (*node)->child[l]->child[r];
        left->child[r] = *node;
        *node = left;
    }
}
int AVL_set_inside_update(AVL_set **node, ll data, int add){
    if(*node == NULL){
        if(add==2){
            *node = malloc(sizeof(AVL_set));
            (*node)->val = data;
            (*node)->cnt = 1;
            (*node)->diff = 0;
            (*node)->child[0] = NULL;
            (*node)->child[1] = NULL;
        }
        return add==2 ? *node != NULL : 0; 
    }else{
        int l, delta, delta_sign; AVL_set *next_node;
        if(data == (*node)->val){
            if(add==2){
                (*node)->cnt++;
                return 0;
            }else{
                if( add && (*node)->cnt > 1 ){
                    (*node)->cnt--; return 0;
                }else{
                    if((*node)->child[1] == NULL){
                        next_node = (*node)->child[0];
                        free(*node);
                        *node = next_node;
                        return -1;
                    }else if((*node)->child[0] == NULL){
                        next_node = (*node)->child[1];
                        free(*node);
                        *node = next_node;
                        return -1;
                    }else{
                        for(next_node = (*node)->child[0];
                        next_node->child[1] != NULL;
                        next_node = next_node->child[1]);
                        (*node)->val = next_node->val;
                        l=0;
                        delta_sign=1;
                        delta = AVL_set_inside_update(&(*node)->child[l], next_node->val, add);
                    }
                }
            }
        }else{
            l = data >= (*node)->val ? 1 : 0;
            delta_sign = data < (*node)->val ? 1 : -1;
            delta = AVL_set_inside_update(&(*node)->child[l], data, add);
        }
        if( delta ){
            int orig_diff = (*node)->diff;
            int do_rotate = 0, rotate_l , diff_sign , rotate_right;
            (*node)->diff += delta * delta_sign;
            if((*node)->diff > 1){
                do_rotate = 1;
                rotate_l = 0;
                diff_sign = 1;
                rotate_right = 1;
            }else if((*node)->diff < -1){
                do_rotate = 1;
                rotate_l = 1;
                diff_sign = -1;
                rotate_right = 0;
            }
            if(do_rotate){
                int child_diff = (*node)->child[rotate_l]->diff;
                if((*node)->child[rotate_l]->diff * diff_sign < 0){
                    AVL_set_inside_rotate(&(*node)->child[rotate_l], !rotate_right);
                }
                AVL_set_inside_rotate(node, rotate_right);
                return delta < 0 && child_diff != 0 ? -1 : 0;
            }
            if     (delta > 0 && orig_diff == 0) return 1;
            else if(delta < 0 && orig_diff != 0) return -1;
            else                                 return 0;
        }else{ 
            return 0;
        }
    }
}

void AVL_set_inside_print(const AVL_set *node, int depth){
    if(node == NULL) return;
    AVL_set_inside_print(node->child[1], depth + 1);
    printf("%lld %d\n", node->val,node->cnt);
    AVL_set_inside_print(node->child[0], depth + 1);    
}
void AVL_set_inside_free(AVL_set *node){
    if(node == NULL) return;
    AVL_set_inside_free(node->child[0]);
    AVL_set_inside_free(node->child[1]);
    free(node);
}
ll AVL_set_inside_count(AVL_set *root, ll val){
    AVL_set *node; node = root;
    while(node){
        if     (val < node->val) node = node->child[0];
        else if(val > node->val) node = node->child[1];
        else                     return node->cnt;
    }
    return 0;
}


/*----------------------------under construction------------------------*/
int AVL_set_lowcomp(ll node, ll val, int type){
    if(node==val){
        if(type!=3) return 0;
        else return 1;
    }
    if(node<val){
        return 1;
    }
    if(node>val){
        return -1;
    }
    return 0;
}
// return smallest p  which meets  a[p]==val :1  >=:2   >:3
AVL_set* AVL_set_inside_lowerbound(AVL_set *root, ll val, int type){
    AVL_set *node; node = root;
    while(node){
        int com=AVL_set_lowcomp(node->val,val,type);
        // printf("%lld %d\n",node->val,com);
        if(com==0) return node;
        if(com==1) node = node->child[1];
        if(com==-1){
            AVL_set *small;
            small=AVL_set_inside_lowerbound(node->child[0],val,type);
            if(type==1){
                return small;
            }else{
                if(small!=NULL) return small;
                else return node;                 
            }
        }
    }
    return node;
}

int AVL_set_upcomp(ll node, ll val, int type){
    if(node==val){
        if(type!=3) return 0;
        else return -1;
    }
    if(node<val){
        return 1;
    }
    if(node>val){
        return -1;
    }
    return 0;
}
// return biggest p  which meets   a[p]==val :1  <=:2   <:3
AVL_set* AVL_set_inside_upperbound(AVL_set *root, ll val, int type){
    AVL_set *node; node = root;
    while(node){
        int com=AVL_set_upcomp(node->val,val,type);
        // printf("%lld %d\n",node->val,com);
        if(com==0) return node;
        if(com==-1) node = node->child[0];
        if(com==1){
            AVL_set *big;
            big=AVL_set_inside_upperbound(node->child[1],val,type);
            if(type==1){
                return big;
            }else{
                if(big!=NULL) return big;
                else return node;                 
            }
        }
    }
    return node;
}
/*----------------------------under construction------------------------*/


ll AVL_set_inside_minmax(AVL_set *root, int type){
    while(root->child[type] !=NULL)  root= root->child[type];
    return root->val;
}
void AVL_set_inside_swap(AVL_set **node1, AVL_set **node2){  
    AVL_set *tmp;  tmp=*node1; *node1=*node2; *node2=tmp;
}

#define set_MAX_SIZE 514511
ll set_main( int command , int set_num , ll val ,ll option){
    static bool set_is_init=false;
    static AVL_set *set_pointer[set_MAX_SIZE];
    static ll set_siz[set_MAX_SIZE];
    if(!set_is_init){ set_is_init=true; rep(i,0,set_MAX_SIZE){ *(set_pointer+i) = NULL; set_siz[i]=0; } }
    if(command==-1){ AVL_set_inside_print( set_pointer[set_num] ,0); }
    if(command==1){ AVL_set_inside_count(set_pointer[set_num],val) ? 1 : set_siz[set_num]++;  AVL_set_inside_update( &set_pointer[set_num] , val , 2 ); }
    if(command==2){ return AVL_set_inside_count(set_pointer[set_num],val); }
    if(command==3){ ( AVL_set_inside_count(set_pointer[set_num],val) > 1 ) ? 1 : set_siz[set_num]--;  AVL_set_inside_update( &set_pointer[set_num] , val,1); }
    if(command==4){ set_siz[set_num]--; AVL_set_inside_update( &set_pointer[set_num] , val , 0 ); }
    if(command==5){ set_siz[set_num]=0; AVL_set_inside_free( set_pointer[set_num] ); set_pointer[set_num] = NULL; }
    if(command==6){ return set_siz[set_num]; }
    if(command==7){ return AVL_set_inside_minmax(set_pointer[set_num],1); }
    if(command==8){ return AVL_set_inside_minmax(set_pointer[set_num],0); }
    if(command==9){ AVL_set_inside_swap(&set_pointer[set_num],&set_pointer[val]); }
    if(10<=command&&command<=12){
        AVL_set *lowbound = AVL_set_inside_lowerbound(set_pointer[set_num],val,command-9);
        if(lowbound==NULL) return option;
        else return lowbound->val;
    }
    if(13<=command&&command<=15){
        AVL_set *upbound = AVL_set_inside_upperbound(set_pointer[set_num],val,command-9);
        if(upbound==NULL) return option;
        else return upbound->val;
    }
    return 0;
}

void set_print(int set_num){ set_main(-1,set_num,0,0); }
void set_insert(int set_num, ll val){ set_main(1,set_num,val,0); }
ll set_count(int set_num, ll val){ return set_main(2,set_num,val,0); }
void set_erase(int set_num, ll val, int is_all){ if(is_all) set_main(4,set_num,val,0); else set_main(3,set_num,val,0); }
void set_clear(int set_num){ set_main(5,set_num,0,0); }
ll set_size(int set_num){ return set_main(6,set_num,0,0); }
ll set_max(int set_num){ return set_main(7,set_num,0,0); }
ll set_min(int set_num){ return set_main(8,set_num,0,0); }
void set_swap(int set_num1, int set_num2){ set_main(9,set_num1,set_num2,0); }


// return smallest p  which meets  a[p]==val :1  >=:2   >:3
ll set_lowerbound(int set_num, ll val, int type, ll error){
    return set_main(9+type,set_num,val,error);
}
// return biggest p  which meets   a[p]==val :1  <=:2   <:3
ll set_upperbound(int set_num, ll val, int type, ll error){
    return set_main(12+type,set_num,val,error);
}

/*
insert *
size *
clear *
erase *
count *
max *
min *
swap *
begin
end
merge  source の要素のキーと等価なキーの要素がある場合、その要素は source から抽出されない
lower_bound
upper_bound
*/

// ll map_main()

/*---------------------------AVL start--------------------------------*/

#pragma endregion AVL



#pragma endregion kyopuro_templates













char s[1151154];
ll fl[225225];
void solve(){
    // fgets(s,sizeof(s),stdin); 
    ll n;
    ll ans=0;
    cin(&n);
    // scanf("%s",s);
    ll h[n];
    ll a[n];
    rep(i,0,n){
        cin(&h[i]);
    }
    rep(i,0,n){
        cin(&a[i]);
    }
    set_insert(0,0);
    ll tmp=POW(10,10);
    rep(i,0,n){
        ll p=set_upperbound(0,h[i]*tmp,3,-1);
        // ll p=upper_bound(fl,0,cnt-1,h[i]*tmp,3);
        // printf("i&p:%lld %lld\n",i,p);
        assert(p!=-1);
        assert(h[i]!=p/tmp);
        ll val=p%tmp+a[i];
        while(1){
            ll q=set_lowerbound(0,h[i]*tmp,2,-1);
            if(q==-1){
                set_insert(0,h[i]*tmp+val);
                break;
            }
            if(q/tmp==h[i]){
                if(q%tmp>=val){
                    break;
                }else{
                    set_erase(0,q,1);
                }
            }else{
                if(q%tmp>val){
                    set_insert(0,h[i]*tmp+val);
                    break;  
                }else{
                    set_erase(0,q,1);
                }
            }
        }
    }
    printf("%lld\n",set_max(0)%tmp);
}

int main(void){
    ll T=1;
    // cin(&T);
    rep(i,0,T){ solve(); }
    return 0;
}


/*
    while (ng + 1 < ok) {
        ll p = ng + (ok - ng) / 2;
        ll cnt = 0;
        rep(i,0,n){
            cnt += (a[i] + p - 1) / p - 1;
        }
        if (cnt <= k) ok = p; else ng = p;
    }
*/
// 10^18 2^60 3^38 5^26