#include <bits/stdc++.h>
using namespace std;
using int128  = __int128_t;
using int64   = long long;
using int32   = int;
using uint128 = __uint128_t;
using uint64  = unsigned long long;
using uint32  = unsigned int;

#define ALL(obj) (obj).begin(),(obj).end()
template<class T> using priority_queue_reverse = priority_queue<T,vector<T>,greater<T>>;

constexpr int64 MOD = 1'000'000'000LL + 7; //'
constexpr int64 MOD2 = 998244353;
constexpr int64 HIGHINF = 1'000'000'000'000'000'000LL;
constexpr int64 LOWINF = 1'000'000'000'000'000LL; //'
constexpr long double PI = 3.1415926535897932384626433L;

template <class T> vector<T> multivector(size_t N,T init){return vector<T>(N,init);}
template <class... T> auto multivector(size_t N,T... t){return vector<decltype(multivector(t...))>(N,multivector(t...));}
template <class T> void corner(bool flg, T hoge) {if (flg) {cout << hoge << endl; exit(0);}}
template <class T, class U>ostream &operator<<(ostream &o, const map<T, U>&obj) {o << "{"; for (auto &x : obj) o << " {" << x.first << " : " << x.second << "}" << ","; o << " }"; return o;}
template <class T>ostream &operator<<(ostream &o, const set<T>&obj) {o << "{"; for (auto itr = obj.begin(); itr != obj.end(); ++itr) o << (itr != obj.begin() ? ", " : "") << *itr; o << "}"; return o;}
template <class T>ostream &operator<<(ostream &o, const multiset<T>&obj) {o << "{"; for (auto itr = obj.begin(); itr != obj.end(); ++itr) o << (itr != obj.begin() ? ", " : "") << *itr; o << "}"; return o;}
template <class T>ostream &operator<<(ostream &o, const vector<T>&obj) {o << "{"; for (int i = 0; i < (int)obj.size(); ++i)o << (i > 0 ? ", " : "") << obj[i]; o << "}"; return o;}
template <class T>ostream &operator<<(ostream &o, const deque<T>&obj) {o << "{"; for (int i = 0; i < (int)obj.size(); ++i)o << (i > 0 ? ", " : "") << obj[i]; o << "}"; return o;}
template <class T, class U>ostream &operator<<(ostream &o, const pair<T, U>&obj) {o << "{" << obj.first << ", " << obj.second << "}"; return o;}
void print(void) {cout << endl;}
template <class Head> void print(Head&& head) {cout << head;print();}
template <class Head, class... Tail> void print(Head&& head, Tail&&... tail) {cout << head << " ";print(forward<Tail>(tail)...);}
template <class T> void chmax(T& a, const T b){a=max(a,b);}
template <class T> void chmin(T& a, const T b){a=min(a,b);}
vector<string> split(const string &str, const char delemiter) {vector<string> res;stringstream ss(str);string buffer; while( getline(ss, buffer, delemiter) ) res.push_back(buffer); return res;}
inline constexpr int msb(int x) {return x?31-__builtin_clz(x):-1;}
inline constexpr int64 ceil_div(const int64 a,const int64 b) {return (a+(b-1))/b;}// return ceil(a/b)
void YN(bool flg) {cout << (flg ? "YES" : "NO") << endl;}
void Yn(bool flg) {cout << (flg ? "Yes" : "No") << endl;}
void yn(bool flg) {cout << (flg ? "yes" : "no") << endl;}

/*
 * @title Graph
 * @docs md/graph/Graph.md
 */
template<class T> class Graph{
private:
    const size_t N,H,W;
public:
    vector<vector<pair<size_t,T>>> edges;
    Graph(const size_t N):H(-1),W(-1),N(N), edges(N) {}
    Graph(const size_t H, const size_t W):H(H),W(W),N(H*W), edges(H*W) {}
    inline void make_edge(size_t from, size_t to, T w) {
        edges[from].emplace_back(to,w);
    }
    //{from_y,from_x} -> {to_y,to_x} 
    inline void make_edge(pair<size_t,size_t> from, pair<size_t,size_t> to, T w) {
        make_edge(from.first*W+from.second,to.first*W+to.second,w);
    }
    inline void make_bidirectional_edge(size_t from, size_t to, T w) {
        make_edge(from,to,w);
        make_edge(to,from,w);
    }
    inline void make_bidirectional_edge(pair<size_t,size_t> from, pair<size_t,size_t> to, T w) {
        make_edge(from.first*W+from.second,to.first*W+to.second,w);
        make_edge(to.first*W+to.second,from.first*W+from.second,w);
    }
    inline size_t size(){return N;}
    inline size_t idx(pair<size_t,size_t> yx){return yx.first*W+yx.second;}
};

/*
 * @title LazySegmentTree - 非再帰抽象化遅延評価セグメント木
 * @docs md/segment/LazySegmentTree.md
 */
template<class Operator> class LazySegmentTree {
	using TypeNode = typename Operator::TypeNode;          
	using TypeLazy = typename Operator::TypeLazy;
	size_t num;      
	size_t length;                                   
	size_t height;                                   
	vector<TypeNode> node;                           
	vector<TypeLazy> lazy;                           
	vector<pair<size_t,size_t>> range;

	void propagate(int k) {
		if(lazy[k] == Operator::unit_lazy) return;
        node[k] = Operator::func_merge(node[k],lazy[k],range[k].first,range[k].second);
		if(k < length) lazy[2*k+0] = Operator::func_lazy(lazy[2*k+0],lazy[k]);
		if(k < length) lazy[2*k+1] = Operator::func_lazy(lazy[2*k+1],lazy[k]);
		lazy[k] = Operator::unit_lazy;
	}
public:

	//unitで初期化
	LazySegmentTree(const size_t num) : num(num) {
		for (length = 1,height = 0; length <= num; length *= 2, height++);
		node.resize(2 * length, Operator::unit_node);
		lazy.resize(2 * length, Operator::unit_lazy);
		for (int i = 0; i < num; ++i) node[i + length] = Operator::unit_node;
		for (int i = length - 1; i >= 0; --i) node[i] = Operator::func_node(node[(i<<1)+0],node[(i<<1)+1]);
		range.resize(2 * length);
		for (int i = 0; i < length; ++i) range[i+length] = make_pair(i,i+1);
		for (int i = length - 1; i >= 0; --i) range[i] = make_pair(range[(i<<1)+0].first,range[(i<<1)+1].second);
	}

	// //同じinitで初期化
	LazySegmentTree(const size_t num, const TypeNode init) : num(num) {
		for (length = 1,height = 0; length <= num; length *= 2, height++);
		node.resize(2 * length, Operator::unit_node);
		lazy.resize(2 * length, Operator::unit_lazy);
		for (int i = 0; i < num; ++i) node[i + length] = init;
		for (int i = length - 1; i >= 0; --i) node[i] = Operator::func_node(node[(i<<1)+0],node[(i<<1)+1]);
		range.resize(2 * length);
		for (int i = 0; i < length; ++i) range[i+length] = make_pair(i,i+1);
		for (int i = length - 1; i >= 0; --i) range[i] = make_pair(range[(i<<1)+0].first,range[(i<<1)+1].second);
	}

	//vectorで初期化
	LazySegmentTree(const vector<TypeNode>& vec) : num(vec.size()) {
		for (length = 1,height = 0; length <= vec.size(); length *= 2, height++);
		node.resize(2 * length, Operator::unit_node);
		lazy.resize(2 * length, Operator::unit_lazy);
		for (int i = 0; i < vec.size(); ++i) node[i + length] = vec[i];
		for (int i = length - 1; i >= 0; --i) node[i] = Operator::func_node(node[(i<<1)+0],node[(i<<1)+1]);
		range.resize(2 * length);
		for (int i = 0; i < length; ++i) range[i+length] = make_pair(i,i+1);
		for (int i = length - 1; i >= 0; --i) range[i] = make_pair(range[(i<<1)+0].first,range[(i<<1)+1].second);
	}

	//update [a,b)
	void update(int a, int b, TypeLazy x) {
		int l = a + length, r = b + length - 1;
		for (int i = height; 0 < i; --i) propagate(l >> i), propagate(r >> i);
		for(r++; l < r; l >>=1, r >>=1) {
			if(l&1) lazy[l] = Operator::func_lazy(lazy[l],x), propagate(l),l++;
			if(r&1) --r,lazy[r] = Operator::func_lazy(lazy[r],x), propagate(r);
		}
		l = a + length, r = b + length - 1;
		while ((l>>=1),(r>>=1),l) {
            if(lazy[l] == Operator::unit_lazy) node[l] = Operator::func_node(Operator::func_merge(node[(l<<1)+0],lazy[(l<<1)+0],range[(l<<1)+0].first,range[(l<<1)+0].second),Operator::func_merge(node[(l<<1)+1],lazy[(l<<1)+1],range[(l<<1)+1].first,range[(l<<1)+1].second));
            if(lazy[r] == Operator::unit_lazy) node[r] = Operator::func_node(Operator::func_merge(node[(r<<1)+0],lazy[(r<<1)+0],range[(r<<1)+0].first,range[(r<<1)+0].second),Operator::func_merge(node[(r<<1)+1],lazy[(r<<1)+1],range[(r<<1)+1].first,range[(r<<1)+1].second));
  		}
	}

	//get [a,b)
	TypeNode get(int a, int b) {
		int l = a + length, r = b + length - 1;
		for (int i = height; 0 < i; --i) propagate(l >> i), propagate(r >> i);
		TypeNode vl = Operator::unit_node, vr = Operator::unit_node;
		for(r++; l < r; l >>=1, r >>=1) {
            if(l&1) vl = Operator::func_node(vl,Operator::func_merge(node[l],lazy[l],range[l].first,range[l].second)),l++;
            if(r&1) r--,vr = Operator::func_node(Operator::func_merge(node[r],lazy[r],range[r].first,range[r].second),vr);
 		}
		return Operator::func_node(vl,vr);
	}

	//return [0,length]
	int prefix_binary_search(TypeNode var) {
		int l = length, r = 2*length - 1;
		for (int i = height; 0 < i; --i) propagate(l >> i), propagate(r >> i);
		if(!Operator::func_check(node[1],var)) return num;
		TypeNode ret = Operator::unit_node;
		size_t idx = 2;
		for(; idx < 2*length; idx<<=1){
            if(!Operator::func_check(Operator::func_node(ret,Operator::func_merge(node[idx],lazy[idx],range[idx].first,range[idx].second)),var)) {
                ret = Operator::func_node(ret,Operator::func_merge(node[idx],lazy[idx],range[idx].first,range[idx].second));
                idx++;
            }
		}
		return min((idx>>1) - length,num);
	}

	//range[l,r) return [l,r]
	int binary_search(size_t l, size_t r, TypeNode var) {
		if (l < 0 || length <= l || r < 0 || length < r) return -1;
		for (int i = height; 0 < i; --i) propagate((l+length) >> i), propagate((r+length-1) >> i);
		TypeNode ret = Operator::unit_node;
		size_t off = l;
		for(size_t idx = l+length; idx < 2*length && off < r; ){
            if(range[idx].second<=r && !Operator::func_check(Operator::func_node(ret,Operator::func_merge(node[idx],lazy[idx],range[idx].first,range[idx].second)),var)) {
                ret = Operator::func_node(ret,Operator::func_merge(node[idx],lazy[idx],range[idx].first,range[idx].second));
                off = range[idx++].second;
                if(!(idx&1)) idx >>= 1;			
            }
            else{
				idx <<=1;
			}
		}
		return off;
	}

	void print(){
		// cout << "node" << endl;
		// for(int i = 1,j = 1; i < 2*length; ++i) {
		// 	cout << node[i] << " ";
		// 	if(i==((1<<j)-1) && ++j) cout << endl;
		// }
		// cout << "lazy" << endl;
		// for(int i = 1,j = 1; i < 2*length; ++i) {
		// 	cout << lazy[i] << " ";
		// 	if(i==((1<<j)-1) && ++j) cout << endl;
		// }
		cout << "vector" << endl;
		cout << "{ " << get(0,1);
		for(int i = 1; i < length; ++i) cout << ", " << get(i,i+1);
		cout << " }" << endl;
	}
};

//node:総和　lazy:加算
template<class T, class U> struct NodeSumRangeAdd {
	using TypeNode = T;
	using TypeLazy = U;
	inline static constexpr TypeNode unit_node = 0;
	inline static constexpr TypeLazy unit_lazy = 0;
	inline static constexpr TypeNode func_node(TypeNode l,TypeNode r){return l+r;}
	inline static constexpr TypeLazy func_lazy(TypeLazy old_lazy,TypeLazy new_lazy){return old_lazy+new_lazy;}
	inline static constexpr TypeNode func_merge(TypeNode node,TypeLazy lazy,int l, int r){return node+lazy*(r-l);}
	inline static constexpr bool func_check(TypeNode nodeVal,TypeNode var){return var <= nodeVal;}
	// LazySegmentTree<NodeSumRangeUpdate<ll,ll>> Seg(N,0);
};

/*
 * @title Tree - 木
 * @docs md/graph/Tree.md
 */
template<class Operator> class TreeBuilder;
template<class Operator> class Tree {
private:
	using TypeEdge = typename Operator::TypeEdge;
	size_t num;
	size_t ord;
	Graph<TypeEdge>& g;
	friend TreeBuilder<Operator>;
	Tree(Graph<TypeEdge>& graph):
		g(graph),
		num(graph.size()),
		depth(graph.size(),-1),
		order(graph.size()),
		edge_dist(graph.size()){
	}
	//for make_depth
	void dfs(int curr, int prev){
		for(const auto& e:g.edges[curr]){
			const int& next = e.first;
			if(next==prev) continue;
			depth[next] = depth[curr] + 1;
			edge_dist[next]  = Operator::func_edge_merge(edge_dist[curr],e.second);
			dfs(next,curr);
			order[ord++] = next;
		}
	}
	//for make_eulertour
	void dfs(int from){
		eulertour.push_back(from);
		for(auto& e:child[from]){
			int to = e.first;            
			dfs(to);        
			eulertour.push_back(from);
		}
	}
	void make_root(const int root) {
		depth[root] = 0;
		edge_dist[root] = Operator::unit_edge;
		ord = 0;
		dfs(root,-1);
		order[ord++] = root;
		reverse_copy(order.begin(),order.end(),back_inserter(reorder));
	}
	void make_root() {
        ord = 0;
        for(int i=0;i<num;++i) {
            if(depth[i]!=-1) continue;
            depth[i] = 0;
            edge_dist[i] = Operator::unit_edge;
            dfs(i,-1);
            order[ord++] = i;
        }
		reverse_copy(order.begin(),order.end(),back_inserter(reorder));
	}
	void make_child(const int root = 0) {
		child.resize(num);
		for (size_t i = 0; i < num; ++i) for (auto& e : g.edges[i]) if (depth[i] < depth[e.first]) child[i].push_back(e);
	}
	void make_subtree_size() {
		subtree_size.resize(num,1);
		for (size_t i:order) for (auto e : child[i]) subtree_size[i] += subtree_size[e.first];
	}
	void make_parent() {
		parent.resize(num,make_pair(num,Operator::unit_edge));
		for (size_t i = 0; i < num; ++i) for (auto& e : g.edges[i]) if (depth[i] > depth[e.first]) parent[i] = e;
	}
	void make_ancestor() {
		ancestor.resize(num);
		for (size_t i = 0; i < num; ++i) ancestor[i][0] = (parent[i].first!=num?parent[i]:make_pair(i,Operator::unit_lca_edge));
		for (size_t j = 1; j < Operator::bit; ++j) {
			for (size_t i = 0; i < num; ++i) {
				size_t k = ancestor[i][j - 1].first;
				ancestor[i][j] = Operator::func_lca_edge_merge(ancestor[k][j - 1],ancestor[i][j - 1]);
			}
		}
	}
	pair<size_t,TypeEdge> lca_impl(size_t l, size_t r) {
		if (depth[l] < depth[r]) swap(l, r);
		int diff = depth[l] - depth[r];
		auto ancl = make_pair(l,Operator::unit_lca_edge);
		auto ancr = make_pair(r,Operator::unit_lca_edge);
		for (int j = 0; j < Operator::bit; ++j) {
			if (diff & (1 << j)) ancl = Operator::func_lca_edge_merge(ancestor[ancl.first][j],ancl);
		}
		if(ancl.first==ancr.first) return ancl;
		for (int j = Operator::bit - 1; 0 <= j; --j) {
			if(ancestor[ancl.first][j].first!=ancestor[ancr.first][j].first) {
				ancl = Operator::func_lca_edge_merge(ancestor[ancl.first][j],ancl);
				ancr = Operator::func_lca_edge_merge(ancestor[ancr.first][j],ancr);
			}
		}
		ancl = Operator::func_lca_edge_merge(ancestor[ancl.first][0],ancl);
		ancr = Operator::func_lca_edge_merge(ancestor[ancr.first][0],ancr);
		return Operator::func_lca_edge_merge(ancl,ancr);
	}
	pair<TypeEdge,vector<size_t>> diameter_impl() {
		Tree tree = Tree::builder(g).build();
		size_t root = 0;
		{
			tree.make_root(0);
		}
		root = max_element(tree.edge_dist.begin(),tree.edge_dist.end()) - tree.edge_dist.begin();
		{
			tree.make_root(root);
		}
		size_t leaf = max_element(tree.edge_dist.begin(),tree.edge_dist.end()) - tree.edge_dist.begin();
		TypeEdge sz = tree.edge_dist[leaf];
		vector<size_t> st;
		{
			tree.make_parent();
			while(leaf != root) {
				st.push_back(leaf);
				leaf = tree.parent[leaf].first;
			}
			st.push_back(root);
		}
		return make_pair(sz,st);
	}
	template<class TypeReroot> vector<TypeReroot> rerooting_impl(vector<TypeReroot> rerootdp,vector<TypeReroot> rerootparent) {
		for(size_t pa:order) for(auto& e:child[pa]) rerootdp[pa] = Operator::func_reroot_dp(rerootdp[pa],rerootdp[e.first]);
		for(size_t pa:reorder) {
			if(depth[pa]) rerootdp[pa] = Operator::func_reroot_dp(rerootdp[pa],rerootparent[pa]);
			size_t m = child[pa].size();
			for(int j = 0; j < m && depth[pa]; ++j){
				size_t ch = child[pa][j].first;
				rerootparent[ch] = Operator::func_reroot_dp(rerootparent[ch],rerootparent[pa]);
			}
			if(m <= 1) continue;
			vector<TypeReroot> l(m),r(m);
			for(int j = 0; j < m; ++j) {
				size_t ch = child[pa][j].first;
				l[j] = rerootdp[ch];
				r[j] = rerootdp[ch];
			}
			for(int j = 1; j+1 < m; ++j) l[j] = Operator::func_reroot_merge(l[j],l[j-1]);
			for(int j = m-2; 0 <=j; --j) r[j] = Operator::func_reroot_merge(r[j],r[j+1]);
			size_t chl = child[pa].front().first;
			size_t chr = child[pa].back().first;
			rerootparent[chl] = Operator::func_reroot_dp(rerootparent[chl],r[1]);
			rerootparent[chr] = Operator::func_reroot_dp(rerootparent[chr],l[m-2]);
			for(int j = 1; j+1 < m; ++j) {
				size_t ch = child[pa][j].first;
				rerootparent[ch] = Operator::func_reroot_dp(rerootparent[ch],l[j-1]);
				rerootparent[ch] = Operator::func_reroot_dp(rerootparent[ch],r[j+1]);
			}
		}
		return rerootdp;
	}
	void make_eulertour() {
		dfs(reorder.front());
		eulertour_range.resize(num);
		for(int i = 0; i < eulertour.size(); ++i) eulertour_range[eulertour[i]].second = i+1;
		for(int i = eulertour.size()-1; 0 <= i; --i) eulertour_range[eulertour[i]].first = i;
	}
	void make_heavy_light_decomposition(){
		head.resize(num);
		hld.resize(num);
		iota(head.begin(),head.end(),0);
		for(size_t& pa:reorder) {
			pair<size_t,size_t> maxi = {0,num};
			for(auto& p:child[pa]) maxi = max(maxi,{subtree_size[p.first],p.first});
			if(maxi.first) head[maxi.second] = head[pa];
		}
		stack<size_t> st_head,st_sub;
		size_t cnt = 0;
		//根に近い方から探索
		for(size_t& root:reorder){
			if(depth[root]) continue;
			//根をpush
			st_head.push(root);
			while(st_head.size()){
				size_t h = st_head.top();
				st_head.pop();
				//部分木の根をpush
				st_sub.push(h);
				while (st_sub.size()){
					size_t pa = st_sub.top();
					st_sub.pop();
					//部分木をカウントしていく
					hld[pa] = cnt++;
					//子を探索
					for(auto& p:child[pa]) {
						//子のheadが親と同じなら、そのまま進む
						if(head[p.first]==head[pa]) st_sub.push(p.first);
						//そうじゃない場合は、そこから新しく部分木としてみなす
						else st_head.push(p.first);
					}
				}				
			}
		}
	}
	//type 0: vertex, 1: edge
	vector<pair<size_t,size_t>> path_impl(size_t u,size_t v,int type = 0) {
		vector<pair<size_t,size_t>> path;
		while(1){
			if(hld[u]>hld[v]) swap(u,v);
			if(head[u]!=head[v]) {
				path.push_back({hld[head[v]],hld[v]});
				v=parent[head[v]].first;
			}
			else {
				path.push_back({hld[u],hld[v]});
				break;
			}
		}
		reverse(path.begin(),path.end());
		if(type) path.front().first++;
		return path;
	}
	size_t lca_idx_impl(size_t u,size_t v){
		while(1){
			if(hld[u]>hld[v]) swap(u,v);
			if(head[u]==head[v]) return u;
			v=parent[head[v]].first;
		}
	}
	vector<size_t> head;
public:
	vector<size_t> depth;
	vector<size_t> order;
	vector<size_t> reorder;
	vector<size_t> subtree_size;
	vector<pair<size_t,TypeEdge>> parent;
	vector<vector<pair<size_t,TypeEdge>>> child;
	vector<TypeEdge> edge_dist;
	vector<array<pair<size_t,TypeEdge>,Operator::bit>> ancestor;
	vector<size_t> eulertour;
	vector<pair<size_t,size_t>> eulertour_range;
	vector<size_t> hld;

	/**
	 * O(N) builder
	 */
	static TreeBuilder<Operator> builder(Graph<TypeEdge>& graph) { return TreeBuilder<Operator>(graph);}
	/**
	 * O(logN) after make_ancestor
	 * return {lca,lca_dist} l and r must be connected 
	 */
	pair<size_t,TypeEdge> lca(size_t l, size_t r) {return lca_impl(l,r);}
	/**
	 * O(N) anytime
	 * return {diameter size,diameter set} 
	 */
	pair<TypeEdge,vector<size_t>> diameter(void){return diameter_impl();}
	/**
	 * O(N) after make_child
	 */
	template<class TypeReroot> vector<TypeReroot> rerooting(const vector<TypeReroot>& rerootdp,const vector<TypeReroot>& rerootparent) {return rerooting_impl(rerootdp,rerootparent);}
	/**
	 * O(logN) 
	 * lca(u,v)=u あるいは lca(u,v)=v のときは、根側から順方向パスを返してくれる 
	 */
	vector<pair<size_t,size_t>> vertex_set_on_path(size_t u, size_t v) {return path_impl(u,v,0);}
	/**
	/**
	 * O(logN) 
	 * lca(u,v)=u あるいは lca(u,v)=v のときは、根側から順方向パスを返してくれる 
	 */
	vector<pair<size_t,size_t>> edge_set_on_path(size_t u, size_t v) {return path_impl(u,v,1);}
	/**
	 * O(logN) ancestorのlcaより定数倍軽め。idxだけ
	 */
	size_t lca_idx(size_t u, size_t v) {return lca_idx_impl(u,v);}
};
 
template<class Operator> class TreeBuilder {
	bool is_root_made =false;
	bool is_child_made =false;
	bool is_parent_made=false;
	bool is_subtree_size_made=false;
public:
	using TypeEdge = typename Operator::TypeEdge;
	TreeBuilder(Graph<TypeEdge>& g):tree(g){}
	TreeBuilder& root(const int rt) { is_root_made=true; tree.make_root(rt); return *this;}
	TreeBuilder& root() { is_root_made=true; tree.make_root(); return *this;}
	TreeBuilder& child() { assert(is_root_made); is_child_made=true;  tree.make_child();  return *this;}
	TreeBuilder& parent() { assert(is_root_made); is_parent_made=true; tree.make_parent(); return *this;}
	TreeBuilder& subtree_size() { assert(is_child_made); is_subtree_size_made=true; tree.make_subtree_size(); return *this;}
	TreeBuilder& ancestor() { assert(is_parent_made); tree.make_ancestor(); return *this;}
	TreeBuilder& eulertour() { assert(is_child_made); tree.make_eulertour(); return *this;}
	TreeBuilder& heavy_light_decomposition() { assert(is_subtree_size_made); assert(is_parent_made); tree.make_heavy_light_decomposition(); return *this;}
	Tree<Operator>&& build() {return move(tree);}
private:
	Tree<Operator> tree;
}; 
template<class T> struct TreeOperator{
	using TypeEdge = T;
	inline static constexpr size_t bit = 20;
	inline static constexpr TypeEdge unit_edge = 0;
	inline static constexpr TypeEdge unit_lca_edge = 0;
	inline static constexpr TypeEdge func_edge_merge(const TypeEdge& parent,const TypeEdge& w){return parent+w;}
	inline static constexpr pair<size_t,TypeEdge> func_lca_edge_merge(const pair<size_t,TypeEdge>& l,const pair<size_t,TypeEdge>& r){return make_pair(l.first,l.second+r.second);}
	template<class TypeReroot> inline static constexpr TypeReroot func_reroot_dp(const TypeReroot& l,const TypeReroot& r) {return {l.first+r.first+r.second,l.second+r.second};}
	template<class TypeReroot> inline static constexpr TypeReroot func_reroot_merge(const TypeReroot& l,const TypeReroot& r) {return {l.first+r.first,l.second+r.second};}
};

/**
 * @url 
 * @est
 */ 
int main() {
    cin.tie(0);ios::sync_with_stdio(false);
	int N; cin >> N;
	Graph<int> g(N);
	for(int i=0;i<N-1;++i) {
		int u,v; cin >> u >> v;
		u--,v--;
		g.make_bidirectional_edge(u,v,1);
	}
	auto tree = Tree<TreeOperator<int>>::builder(g).root(0).parent().child().subtree_size().heavy_light_decomposition().build();
	LazySegmentTree<NodeSumRangeAdd<int64,int64>> seg(N);
	int Q; cin >> Q;
	int64 ans = 0;
	while(Q--) {
		int a,b; cin >> a >> b;
		a--,b--;
		auto vp = tree.vertex_set_on_path(a,b);
		for(auto& p:vp) {
			int l = p.first, r = p.second+1;
			int n = r-l;
			ans += seg.get(l,r)+n;
			seg.update(l,r,1);
		}
	}
	cout << ans << endl;
    return 0;
}