This submission is migrated from previous version of oj.uz, which used different machine for grading. This submission may have different result if resubmitted.
#include <bits/stdc++.h>
#define ll long long
#define MAXN 1000010
using namespace std;
ll a[2][MAXN];
pair<ll,ll> dp[2][MAXN];
int main()
{
ios::sync_with_stdio(false); cin.tie(0); cout.tie(0);
ll n;
cin >> n;
for (ll i=0;i<2;i++)
{
for (ll j=1;j<=2*n;j++)
{
cin >> a[i][j];
dp[i][j]={LLONG_MAX,LLONG_MIN};
}
}
dp[0][1]={1,1};
dp[1][1]={0,0};
for (ll i=2;i<=2*n;i++)
{
for (ll j=0;j<2;j++)
{
if (a[0][i]>=a[j][i-1])
{
dp[0][i].first=min(dp[0][i].first,dp[j][i-1].first+1);
dp[0][i].second=max(dp[0][i].second,dp[j][i-1].second+1);
}
if (a[1][i]>=a[j][i-1])
{
dp[1][i].first=min(dp[1][i].first,dp[j][i-1].first);
dp[1][i].second=max(dp[1][i].second,dp[j][i-1].second);
}
}
}
if ((dp[0][2*n].second<n || dp[0][2*n].first>n) && (dp[1][2*n].second<n || dp[1][2*n].first>n))
{
cout << -1 << "\n";
return 0;
}
ll curi,curj=2*n,val=n;
string ans;
curi=dp[0][2*n].first<=n && dp[0][2*n].second>=n?0 : 1;
ans=curi?"B" : "A";
while (curj>1)
{
val-=1-curi;
curi=dp[0][curj-1].first<=val && dp[0][curj-1].second>=val && a[0][curj-1]<=a[curi][curj]?0 : 1;
ans=(curi?'B' : 'A')+ans;
curj--;
}
cout << ans;
return 0;
}
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