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>
#pragma GCC optimize("O3")
using namespace std;
typedef pair<int,int> pii;
typedef long long ll;
const ll baza=29,invbaza=758620695;
const ll mod=1e9+7;
int n;
string s,sol;
vector<char> st;
vector<int> mypoz[27][2][100005];
map<ll,int> nrm;
int nxt[100005];
int sum[100005];
int main()
{
ios_base::sync_with_stdio(false);
cin.tie(0);
cin>>s;
n=s.size();
s=" "+s;
if(n%2==1)
{
cout<<-1;
return 0;
}
int nr=1;
ll h=0;
nrm[h]=1;
sum[0]=1;
for(int i=1;i<=n;i++)
{
if(!st.empty()&&st.back()==s[i])
st.pop_back();
else
st.push_back(s[i]);
}
if(!st.empty())
{
cout<<-1;
return 0;
}
for(int i=1;i<=n;i++)
{
if(!st.empty()&&st.back()==s[i])
{
st.pop_back();
h-=(s[i]-'a'+1);
h=(h*invbaza)%mod;
}
else
{
h=((h*baza)%mod+s[i]-'a'+1)%mod;
st.push_back(s[i]);
}
if(nrm[h]==0)
{
nr++;
nrm[h]=nr;
}
sum[i]=nrm[h];
mypoz[s[i]-'a'+1][i%2][sum[i]].push_back(i);
}
vector<int> last;
sol.resize(n+1);
for(int i=1;i<=n;i++)
{
if(sol[i]!=')')
{
sol[i]='(';
int maxpoz=n+1;
if(!last.empty())
maxpoz=last.back();
int par=1-i%2;
int lit=s[i]-'a'+1;
int lft=0;
int rgt=mypoz[lit][par][sum[i-1]].size();
rgt--;
int poz=0;
while(lft<=rgt)
{
int mij=(lft+rgt)/2;
if(mypoz[lit][par][sum[i-1]][mij]<maxpoz)
{
poz=mypoz[lit][par][sum[i-1]][mij];
lft=mij+1;
}
else
rgt=mij-1;
}
sol[poz]=')';
last.push_back(poz);
}
else
last.pop_back();
}
for(int i=1;i<=n;i++)
cout<<sol[i];
return 0;
}
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