Parsa has a humongous tree on n vertices.

On each vertex v he has written two integers l_v and r_v.

To make Parsa's tree look even more majestic, Nima wants to assign a number a_v (l_v ≤ a_v ≤ r_v) to each vertex v such that the beauty of Parsa's tree is maximized.

Nima's sense of the beauty is rather bizarre. He defines the beauty of the tree as the sum of |a_u - a_v| over all edges (u, v) of the tree.

Since Parsa's tree is too large, Nima can't maximize its beauty on his own. Your task is to find the maximum possible beauty for Parsa's tree.

Input

The first line contains an integer t (1≤ t≤ 250) — the number of test cases. The description of the test cases follows.

The first line of each test case contains a single integer n (2≤ n≤ 10^5) — the number of vertices in Parsa's tree.

The i-th of the following n lines contains two integers l_i and r_i (1 ≤ l_i ≤ r_i ≤ 10^9).

Each of the next n-1 lines contains two integers u and v (1 ≤ u , v ≤ n, u≠ v) meaning that there is an edge between the vertices u and v in Parsa's tree.

It is guaranteed that the given graph is a tree.

It is guaranteed that the sum of n over all test cases doesn't exceed 2 ⋅ 10^5.

Output

For each test case print the maximum possible beauty for Parsa's tree.

Example

Input


3
2
1 6
3 8
1 2
3
1 3
4 6
7 9
1 2
2 3
6
3 14
12 20
12 19
2 12
10 17
3 17
3 2
6 5
1 5
2 6
4 6


Output


7
8
62

Note

The trees in the example:

<image>

In the first test case, one possible assignment is a = \{1, 8\} which results in |1 - 8| = 7.

In the second test case, one of the possible assignments is a = \{1, 5, 9\} which results in a beauty of |1 - 5| + |5 - 9| = 8
import java.io.*;
import java.util.*;

public class Main {
    static PrintWriter pw;
    static Scanner sc;
    static long ceildiv(long x, long y) { return (x+y-1)/y; }
    static int mod(long x, int m) { return (int)((x%m+m)%m); }
    static void put(TreeMap<Integer, Integer> map, Integer p){if(map.containsKey(p)) map.replace(p, map.get(p)+1); else map.put(p, 1); }
    static void rem(TreeMap<Integer, Integer> map, Integer p){ if(map.get(p)==1) map.remove(p);else map.replace(p, map.get(p)-1); }
    static void printf(double x, int dig){ String s="%."+dig+"f"; pw.printf(s, x); }
    static int Int(boolean x){ return x?1:0; }
    static final int inf=(int)1e9, mod= inf+7;
    static final long infL=inf*1l*inf;
    static final double eps=1e-9;
    public static long gcd(long x, long y) { return y==0? x: gcd(y, x%y); }
    public static void main(String[] args) throws Exception {
        sc = new Scanner(System.in);
        pw = new PrintWriter(System.out);
        int t = sc.nextInt();
        while (t-- > 0)
            testcase();
        pw.close();
    }
    static ArrayList<Integer>[] adj;
    static void testcase() throws IOException {
        int n=sc.nextInt();
        Pair[] arr= sc.nextPairArr(n);
        adj=new ArrayList[n];
        for (int i = 0; i < n; i++)
            adj[i]=new ArrayList<>();

        for (int i = 0; i < n-1; i++) {
            int u=sc.nextInt()-1, v=sc.nextInt()-1;
            adj[u].add(v);
            adj[v].add(u);
        }
        dp=new HashMap<>();
        pw.println(dfs(0, -1, -1, arr));
    }
    static HashMap<Triple, Long> dp;
    static long dfs(int i, int par, int parVal, Pair[] arr){
        Triple t=new Triple(i, par, parVal);
        if(!dp.containsKey(t)){
            long ans;
            long a=0, b=0;
            if(par != -1){
                a += Math.abs(arr[i].x-parVal);
                b += Math.abs(arr[i].y - parVal);
            }
            for (int x: adj[i]) {
                if(par == x)
                    continue;
                a+=dfs(x, i, arr[i].x, arr);
                b+=dfs(x, i, arr[i].y, arr);
            }
            ans= Math.max(a, b);
            dp.put(t, ans);
        }
        return dp.get(t);
    }

    static void printArr(int[] arr) {
        for (int i = 0; i < arr.length; i++)
            pw.print(arr[i] + " ");
        pw.println();
    }
    static void printArr(long[] arr) {
        for (int i = 0; i < arr.length; i++)
            pw.print(arr[i] + " ");
        pw.println();
    }
    static void printArr(double[] arr) {
        for (int i = 0; i < arr.length; i++)
            pw.print(arr[i] + " ");
        pw.println();
    }
    static void printArr(Integer[] arr) {
        for (int i = 0; i < arr.length; i++)
            pw.print(arr[i] + " ");
        pw.println();
    }
    static void printArr(ArrayList list) {
        for (int i = 0; i < list.size(); i++)
            pw.print(list.get(i)+" ");
        pw.println();
    }
    static void printArr(boolean[] arr) {
        StringBuilder sb=new StringBuilder();
        for(boolean b: arr)
            sb.append(Int(b));
        pw.println(sb);
    }
    static class Scanner {
        StringTokenizer st;
        BufferedReader br;
        public Scanner(InputStream s) {
            br = new BufferedReader(new InputStreamReader(s));
        }

        public Scanner(FileReader r) {
            br = new BufferedReader(r);
        }

        public String next() throws IOException {
            while (st == null || !st.hasMoreTokens())
                st = new StringTokenizer(br.readLine());
            return st.nextToken();
        }

        public int nextInt() throws IOException {
            return Integer.parseInt(next());
        }

        public long nextLong() throws IOException {
            return Long.parseLong(next());
        }

        public String nextLine() throws IOException {
            return br.readLine();
        }

        public double nextDouble() throws IOException {
            return Double.parseDouble(next());
        }
        public int[] nextDigits() throws IOException{
            String s=nextLine();
            int[] arr=new int[s.length()];
            for(int i=0; i<arr.length; i++)
                arr[i]=s.charAt(i)-'0';
            return arr;
        }
        public int[] nextArr(int n) throws IOException {
            int[] arr = new int[n];
            for (int i = 0; i < arr.length; i++)
                arr[i] = nextInt();
            return arr;
        }
        public Integer[] nextsort(int n) throws IOException{
            Integer[] arr=new Integer[n];
            for(int i=0; i<n; i++)
                arr[i]=nextInt();
            return arr;
        }
        public Pair nextPair() throws IOException{
            return new Pair(nextInt(), nextInt());
        }
        public long[] nextLongArr(int n) throws IOException{
            long[] arr=new long[n];
            for (int i = 0; i < n; i++)
                arr[i]=sc.nextLong();
            return arr;
        }
        public Pair[] nextPairArr(int n) throws IOException{
            Pair[] arr=new Pair[n];
            for(int i=0; i<n; i++)
                arr[i]=nextPair();
            return arr;
        }
        public boolean hasNext() throws IOException {
            return (st!=null && st.hasMoreTokens()) || br.ready();
        }
    }
    static class Pair implements Comparable<Pair> {
        int x;
        int y;

        public Pair(int x, int y) {
            this.x = x;
            this.y = y;
        }

        public Pair(Map.Entry<Integer, Integer> a) {
            x = a.getKey();
            y = a.getValue();
        }

        public boolean contains(int a) {
            return x == a || y == a;
        }

        public int hashCode() {
            return (this.x * 1000000000 + this.y);
        }

        public int compareTo(Pair p) {
            if (x == p.x)
                return y - p.y;
            return x - p.x;
        }

        public boolean equals(Object obj) {
            if (obj == null) {
                return false;
            }
            if (this.getClass() != obj.getClass()) {
                return false;
            }
            Pair p = (Pair) obj;
            return this.x == p.x && this.y == p.y;
        }

        public Pair clone() {
            return new Pair(x, y);
        }

        public String toString() {
            return this.x + " " + this.y;
        }

        public void add(Pair p) {
            x += p.x;
            y += p.y;
        }
    }
    static class LP implements Comparable<LP>{
        long x, y;
        public LP(long a, long b){
            x=a;
            y=b;
        }
        public void add(LP p){
            x+=p.x;
            y+=p.y;
        }
        public boolean equals(LP p){
            return p.x==x && y==p.y;
        }
        public String toString(){
            return this.x+" "+this.y;
        }
        public int compareTo(LP p){
            int a=Long.compare(x, p.x);
            if(a!=0)
                return a;
            return Long.compare(y, p.y);
        }
    }
    static class Triple implements Comparable<Triple>{
        int x, y, z;
        public Triple(int a, int b, int c){
            x=a;
            y=b;
            z=c;
        }
        public int compareTo(Triple t){
            if(this.y!=t.y)
                return y-t.y;
            return x-t.x;
        }
        public String toString(){
            return x+" "+y+" "+z;
        }
        public int hashCode(){
            return new Pair(x, y).hashCode()*1000000000 + z;
        }
        public boolean equals(Object o){
            if(o instanceof Triple){
                Triple t= (Triple) o;
                return t.x==x && t.y==y && t.z==z;
            }
            return false;
        }
    }
}