// Original C++ solution (slower):
#include <bits/stdc++.h>

using namespace std;



#define dump(...) cout<<"# "<<#__VA_ARGS__<<'='<<(__VA_ARGS__)<<endl

#define repi(i,a,b) for(int i=int(a);i<int(b);i++)

#define peri(i,a,b) for(int i=int(b);i-->int(a);)

#define rep(i,n) repi(i,0,n)

#define per(i,n) peri(i,0,n)

#define all(c) begin(c),end(c)

#define mp make_pair

#define mt make_tuple



using uint=unsigned;

using ll=long long;

using ull=unsigned long long;

using vi=vector<int>;

using vvi=vector<vi>;

using vl=vector<ll>;

using vvl=vector<vl>;

using vd=vector<double>;

using vvd=vector<vd>;

using vs=vector<string>;



template<typename T1,typename T2>

ostream& operator<<(ostream& os,const pair<T1,T2>& p){

	return os<<'('<<p.first<<','<<p.second<<')';

}



template<typename Tuple>

void print_tuple(ostream&,const Tuple&){}

template<typename Car,typename... Cdr,typename Tuple>

void print_tuple(ostream& os,const Tuple& t){

	print_tuple<Cdr...>(os,t);

	os<<(sizeof...(Cdr)?",":"")<<get<sizeof...(Cdr)>(t);

}

template<typename... Args>

ostream& operator<<(ostream& os,const tuple<Args...>& t){

	print_tuple<Args...>(os<<'(',t);

	return os<<')';

}



template<typename Ch,typename Tr,typename C>

basic_ostream<Ch,Tr>& operator<<(basic_ostream<Ch,Tr>& os,const C& c){

	os<<'[';

	for(auto i=begin(c);i!=end(c);++i)

		os<<(i==begin(c)?"":" ")<<*i;

	return os<<']';

}



constexpr ll INF=1e18;

constexpr int MOD=1e9+7;

constexpr double EPS=1e-9;



int NextPow2(int x)

{

	x--;

	for(int i=1;i<32;i*=2) x|=x>>i;

	return x+1;

}



template<typename T>

struct SegmentTree{

	const T I=numeric_limits<T>::max();

	T F(T a,T b){return min(a,b);}



	int size;

	vector<T> data;

	SegmentTree(int n):size(NextPow2(n)),data(size*2,I){}

	SegmentTree(const vector<T>& a):size(NextPow2(a.size())),data(size*2,I){

		copy(all(a),begin(data)+size);

		peri(i,1,size) data[i]=F(data[i*2],data[i*2+1]);

	}

	T Get(int i){

		return data[size+i];

	}

	void Update(int i,T x){

		data[size+i]=x;

		for(i+=size;i/=2;) data[i]=F(data[i*2],data[i*2+1]);

	}

	T Query(int a,int b,int i,int l,int r){

		if(b<=l || r<=a) return I;

		if(a<=l && r<=b) return data[i];

		return F(Query(a,b,i*2,l,(l+r)/2),Query(a,b,i*2+1,(l+r)/2,r));

	}

	T Query(int a,int b){

		return Query(a,b,1,0,size);

	}

};



struct Edge{

	int u,v,w;

	Edge(){}

	Edge(int u,int v,int w):u(u),v(v),w(w){}

};

using Tree=vector<vector<Edge>>;



vector<tuple<ll,ll>> dfs(const Tree& t,ll x,int p)

{

	if(t[p].empty()) return {mt(0,0)};	// leaf

	auto e0=t[p][0],e1=t[p][1];

	auto s0=dfs(t,x,e0.v),s1=dfs(t,x,e1.v);



	vector<tuple<ll,ll>> res;

	rep(_,2){

		vl tmp; rep(i,s1.size()) tmp.push_back(get<1>(s1[i]));

		SegmentTree<ll> st(tmp);

		for(int i=0,j=0;i<s0.size();i++){

			ll a,b; tie(a,b)=s0[i];

			for(;j<s1.size();j++){

				ll c,d; tie(c,d)=s1[j];

				if(e0.w+b+c+e1.w>x) break;

			}

			if(j>0){

				ll d=st.Query(0,j);

				res.emplace_back(e0.w+a,d+e1.w);

			}

		}

		swap(e0,e1);

		swap(s0,s1);

	}



	sort(all(res),[](auto a,auto b){return a<b;});

	{

		vector<tuple<ll,ll>> tmp;

		ll cur=INF;

		for(int i=0,j;i<res.size();i=j){

			for(j=i;j<res.size();j++)

				if(get<1>(res[j])<cur)

					break;

			if(j<res.size()){

				cur=get<1>(res[j]);

				tmp.push_back(res[j]);

				j++;

			}

		}

		res=move(tmp);

	}

	return res;

}



bool ok(const Tree& t,ll x)

{

	return dfs(t,x,0).size();

}



int main()

{

	for(int n;cin>>n&&n;){

		Tree t(n);

		rep(i,n-1){

			int u,v=i+1,w; cin>>u>>w; u--;

			t[u].emplace_back(u,v,w);

		}

		ll lo=-1,hi=INF;

		while(hi-lo>1){

			ll mi=(lo+hi)/2;

			(ok(t,mi)?hi:lo)=mi;

		}

		cout<<hi<<endl;

	}

}


// Optimized solution to the same problem (faster):
#include <bits/stdc++.h>

using namespace std;



#define repi(i,a,b) for(int i=int(a);i<int(b);i++)

#define rep(i,n) repi(i,0,n)

#define all(c) begin(c),end(c)

#define mt make_tuple



constexpr int INF=1e9;



struct Edge{

	int u,v,w;

	Edge(){}

	Edge(int u,int v,int w):u(u),v(v),w(w){}

};

using Tree=vector<vector<Edge>>;



vector<tuple<int,int>> dfs(const Tree& t,int x,int p)

{

	if(t[p].empty()) return {mt(0,0)};

	auto e0=t[p][0],e1=t[p][1];

	auto s0=dfs(t,x,e0.v),s1=dfs(t,x,e1.v);



	vector<tuple<int,int>> res;

	rep(_,2){

		for(int i=0,j=0;i<s0.size();i++){

			int a,b; tie(a,b)=s0[i];

			for(;j<s1.size();j++){

				int c,d; tie(c,d)=s1[j];

				if(e0.w+b+c+e1.w>x) break;

			}

			if(j>0){

				int d=get<1>(s1[j-1]);

				res.emplace_back(e0.w+a,d+e1.w);

			}

		}

		swap(e0,e1); swap(s0,s1);

	}



	sort(all(res),[](auto a,auto b){return a<b;});

	res.erase(unique(all(res),[](auto a,auto b){return get<1>(a)<=get<1>(b);}),end(res));

	return res;

}



bool ok(const Tree& t,int x)

{

	return dfs(t,x,0).size();

}



int main()

{

	for(int n;cin>>n&&n;){

		Tree t(n);

		rep(i,n-1){

			int u,v=i+1,w; cin>>u>>w; u--;

			t[u].emplace_back(u,v,w);

		}

		int lo=-1,hi=INF;

		while(hi-lo>1){

			int mi=(lo+hi)/2;

			(ok(t,mi)?hi:lo)=mi;

		}

		cout<<hi<<endl;

	}

}


// Fastest known solution for this problem: