1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
| #include<bits/stdc++.h>
#define ll long long
#define ull unsigned long long
#define maxn 500005
#define put() putchar('\n')
#define Tp template<typename Ty>
#define Ts template<typename Ty,typename... Ar>
using namespace std;
void read(int &x){
int f=1;x=0;char c=getchar();
while (c<'0'||c>'9') {if (c=='-') f=-1;c=getchar();}
while (c>='0'&&c<='9') {x=x*10+c-'0';c=getchar();}
x*=f;
}
namespace Debug{
Tp void _debug(char* f,Ty t){cerr<<f<<'='<<t<<endl;}
Ts void _debug(char* f,Ty x,Ar... y){while(*f!=',') cerr<<*f++;cerr<<'='<<x<<",";_debug(f+1,y...);}
Tp ostream& operator<<(ostream& os,vector<Ty>& V){os<<"[";for(auto& vv:V) os<<vv<<",";os<<"]";return os;}
#define gdb(...) _debug((char*)#__VA_ARGS__,__VA_ARGS__)
}using namespace Debug;
#define fi first
#define se second
#define mk make_pair
const int mod=1e9+7;
int power(int x,int y=mod-2) {
int sum=1;
while (y) {
if (y&1) sum=sum*x%mod;
x=x*x%mod;y>>=1;
}
return sum;
}
pair<int,int> f[maxn*2][2];
int a[maxn*2],b[maxn*2],ans[maxn*2],n;
void dfs(int i,int j,int z) {
ans[i]=z;
j-=(z==0);
if (i==1) return ;
if (z==0) {
if (a[i]>=a[i-1]&&f[i-1][0].fi<=j&&j<=f[i-1][0].se) {
dfs(i-1,j,0);
}
else dfs(i-1,j,1);
}
else {
if (b[i]>=a[i-1]&&f[i-1][0].fi<=j&&j<=f[i-1][0].se) {
dfs(i-1,j,0);
}
else dfs(i-1,j,1);
}
}
void print(void) {
int i;
for (i=1;i<=2*n;i++) putchar(ans[i]==0?'A':'B');
}
signed main(void){
int i,j;
read(n);
for (i=1;i<=2*n;i++) read(a[i]);
for (i=1;i<=2*n;i++) read(b[i]),f[i][0]=f[i][1]=mk(2*n+1,-2*n);
f[0][0]=f[0][1]=mk(0,0);
for (i=1;i<=2*n;i++) {
if (a[i]>=a[i-1]) {
f[i][0].fi=min(f[i][0].fi,f[i-1][0].fi+1);
f[i][0].se=max(f[i][0].se,f[i-1][0].se+1);
}
if (a[i]>=b[i-1]) {
f[i][0].fi=min(f[i][0].fi,f[i-1][1].fi+1);
f[i][0].se=max(f[i][0].se,f[i-1][1].se+1);
}
if (b[i]>=a[i-1]) {
f[i][1].fi=min(f[i][1].fi,f[i-1][0].fi);
f[i][1].se=max(f[i][1].se,f[i-1][0].se);
}
if (b[i]>=b[i-1]) {
f[i][1].fi=min(f[i][1].fi,f[i-1][1].fi);
f[i][1].se=max(f[i][1].se,f[i-1][1].se);
}
}
for (i=0;i<2;i++) if (f[2*n][i].fi<=n&&n<=f[2*n][i].se) {
dfs(2*n,n,i);
print();
return 0;
}
puts("-1");
return 0;
}
|