#include <bits/stdc++.h>
//#pragma GCC optimize ("O3")
//#pragma GCC optimize ("Ofast")
#define F first
#define S second
#define MT make_tuple
#define MP make_pair
#define SZ(a) ((int)(a).size())
#define PB push_back
#define LBS 20
#define MOD ((ll)1224736769)//((ll)((1<<24)+(1<<16)+(1<<8)+1))//((long long)1e9+7) //1e9+9
#define PHIMOD ((ll)MOD-1) //((ll)(1<<24))
#define LEFT(i) (2*(i))
#define RIGHT(i) (2*(i)+1)
#define PAR(i) ((i)/2)
#define ALL(a) (a).begin(), (a).end()
#define END(s) {cout << s;return;}
using namespace std;
typedef int64_t ll;
typedef double rat;
typedef long long bi;
typedef pair<ll, ll> ii;
typedef std::vector<ii> vii;
typedef std::map<ll, ll> mii;
typedef bitset<LBS> bis;
typedef std::vector<bis> vbs;
typedef array<std::vector<ll>, 4> av; //aa,ab,ba,bb
template<class T>
void in(T &a){
for(auto &x: a)
cin >> x;
}
template<class T>
void out(T &a, string sep=" "){
for(auto x: a)
cout << x<<sep;
cout << '\n';
}
template<class T>
void err(T &a, string sep=" "){
for(auto x: a)
cerr << x <<sep;
cerr << '\n';
}
std::vector<std::vector<int> > mp;
ll np2=1, fa;
std::vector<ll> pa;
map<ii,av> miiav;
void fft(std::vector<ll> &v, std::vector<ll> &f, int n, int in){
for(int i=0; i<n; i++)
f[i]=v[mp[__builtin_ctz(n)][i]];
ll t;
for(int l=1; l<n; l*=2)
for(int st=0; st<n; st+=l*2)
for(int i=0; i<l; i++){
t=f[st+i];
f[st+i]=(t+(pa[(np2+in*i*np2/l/2)%np2]*f[st+i+l])%MOD+MOD)%MOD;
f[st+i+l]=(t+(pa[(np2+in*(i+l)*np2/l/2)%np2]*f[st+i+l])%MOD+MOD)%MOD;
}
}
void fftsparse(std::vector<ll> &v, std::vector<ll> &f, int n, char in){
for(int i=0; i<n; i++){
f[i]=0;
for(auto x: v)
f[i]+=pa[(np2+in*(np2/n*x)%np2*i)%np2];
}
}
void rek(const av &a, av &v, int st=0, int l=np2){
if(l==1){
v[0][0]=v[3][0]=1;
miiav[{st,l}][0].PB(0);
miiav[{st,l}][3].PB(0);
return;
}
miiav[{st,l}][0].clear();
if(l==2){
miiav[{st,1}][0].PB(0);
miiav[{st,1}][3].PB(0);
miiav[{st+1,1}][0].PB(0);
miiav[{st+1,1}][3].PB(0);
for(int k=0; k<4; k++)
if (a[k/2][st]<=a[k%2][st+1]) {
v[k][1-k/2]=1;
miiav[{st,l}][k].PB(1-k/2);
}
return;
}
av lv, rv, lf, rf;
for(int i=0; i<4; i++){
lv[i].resize(l,0);
rv[i].resize(l,0);
lf[i].resize(l);
rf[i].resize(l);
}
rek(a,lv,st,l/2);
rek(a,rv,st+l/2,l/2);
for(int i=0; i<4; i++){
if(0 && SZ((miiav[{st,l/2}][i]))<__builtin_ctz(l)*2+3)
fftsparse(miiav[{st,l/2}][i],lf[i],l,1);
else
fft(lv[i], lf[i], l, 1);
if(0 && SZ((miiav[{st+l/2,l/2}][i]))<__builtin_ctz(l)*2+3)
fftsparse(miiav[{st+l/2,l/2}][i],rf[i],l,1);
else
fft(rv[i], rf[i], l, 1);
}
av f;
for(int j=0; j<4; j++){
f[j].resize(l,0);
for(int k=0; k<4; k++)
if(a[k/2][st+l/2-1]<=a[k%2][st+l/2])
for(int i=0; i<l; i++)
f[j][i]+=(lf[(j/2)*2+k/2][i]*((rf[(k%2)*2+j%2][i]*(k/2?1:pa[(np2/l*i)%np2]))%MOD))%MOD;
}
for(int i=0; i<4; i++){
fft(f[i],v[i],l, -1);
for(int j=0; j<l; j++)
if(v[i][j]){
v[i][j]=1;
miiav[{st,l}][i].PB(j);
}
}
}
void path(const av &a, char* s, int an, int dir, int st=0, int l=np2){
if(l==1){
assert(dir==0 || dir==3);
s[st]=(dir==0?'A':'B');
return;
}
assert(miiav.count({st,l/2}) && miiav.count({st+l/2,l/2}));
const av &le=miiav[{st,l/2}], &ri=miiav[{st+l/2, l/2}];
// err(lv);
for(int k=0; k<4; k++)
if(a[k/2][st+l/2-1]<=a[k%2][st+l/2]){
int il=0, ir=SZ(ri[(k%2)*2+dir%2])-1;
while (il<SZ(le[(dir/2)*2+k/2]) && ir>=0) {
int at=le[(dir/2)*2+k/2][il]+(1-k/2)+ri[(k%2)*2+dir%2][ir];
if(at==an){
path(a,s,le[(dir/2)*2+k/2][il],(dir/2)*2+k/2,st,l/2);
path(a,s,ri[(k%2)*2+dir%2][ir],(k%2)*2+dir%2,st+l/2,l/2);
return;
} if(at<an)
il++;
else
ir--;
}
}
//
// for(int i=max((1-k/2),an-l); i<=min(an,l+(1-k/2)); i++)
// if(lv[(dir/2)*2+k/2][i-(1-k/2)] && rv[(k%2)*2+dir%2][an-i]){
// path(a,s,i-(1-k/2),(dir/2)*2+k/2,st,l/2);
// path(a,s,an-i,(k%2)*2+dir%2,st+l/2,l/2);
// return;
// }
assert(1);
}
int main(){
int n; scanf("%d", &n);
n*=2;
while(np2<n)
np2*=2;
av a;
for(int i=0; i<2; i++){
a[i].resize(n);
for(int j=0; j<n; j++)
scanf("%lld", &a[i][j]);
a[i].resize(np2);
}
for(int i=n; i<np2; i++){
a[0][i]=a[0][n-1]+a[1][n-1];
a[1][i]=0;
}
fa=1;
for(int i=0; i<73; i++)
fa=(fa*3)%MOD;
for(int i=1; i<PHIMOD/73/np2; i*=2)
fa=(fa*fa)%MOD;
pa.resize(np2+1);
pa[0]=1;
for(int i=1; i<=np2; i++)
pa[i]=(pa[i-1]*fa)%MOD;
mp.resize(__builtin_ctz(np2)+1);
mp[0].resize(1);
mp[0][0]=0;
for(int i=1; i<SZ(mp); i++){
mp[i].resize(1<<i);
for(int j=0; j<(1<<(i-1)); j++)
mp[i][j]=mp[i-1][j]*2;
for(int j=0; j<(1<<(i-1)); j++)
mp[i][j+(1<<(i-1))]=mp[i-1][j]*2+1;
}
av v;
for(int i=0; i<4; i++)
v[i].resize(np2,0);
rek(a,v);
for(int i=0; i<4; i++)
if(v[i][np2-n/2-(1-i%2)]){
char s[np2*2];
path(a,s,np2-n/2-(1-i%2),i);
s[n]=0;
printf("%s\n", s);
return 0;
}
printf("-1\n");
}
