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.*;
import static java.lang.System.*;
import static java.lang.Math.*;
/**
 * After seeing the solution */

public class HumongusTree
{
	List<Integer>[] tree;
	long[] dp[],L,R;
    void run() {
        int tc=ni();
        StringBuilder sb = new StringBuilder();
        while(tc-->0) {
            int n=ni();
            tree = new ArrayList[n+1];
            L = new long[n+1];
            R = new long[n+1];
            dp = new long[n+1][2];
            for(int i=1;i<=n;i++) tree[i] = new ArrayList<>();
            for(int i=1;i<=n;i++) {
            	L[i]=nl(); R[i]=nl();
            }
            for(int i=0;i<n-1;i++) {
            	int u=ni(),v=ni();
            	tree[u].add(v);
            	tree[v].add(u);
            }
            dfs(1,0);
            sb.append(max(dp[1][0],dp[1][1])).append("\n");
        }
        out.println(sb);
        out.flush(); 
        out.close();
    }

    void dfs(int cur, int par) {
    	// dp[cur][0] = L[cur];
    	// dp[cur][1] = R[cur];
    	for(int child:tree[cur]) {
    		if(child!=par) {
    			dfs(child,cur);
    			dp[cur][0] += max(dp[child][0]+abs(L[cur]-L[child]),dp[child][1]+abs(L[cur]-R[child]));
    			dp[cur][1] += max(dp[child][0]+abs(R[cur]-L[child]),dp[child][1]+abs(R[cur]-R[child]));
    		}
    	}
    }

    public static void main(String[] args)throws Exception {
        try { 
            // new Thread(null, new HumongusTree()::run, "1", 1 << 26).start();
            new Thread(null, new HumongusTree("ONLINE_JUDGE")::run, "1", 1 << 26).start();
        } catch(Exception e) {}
    }

    FastReader sc=null;PrintWriter out = null;
    public HumongusTree()throws Exception {
        sc = new FastReader(new FileInputStream("input.txt"));
        out = new PrintWriter(new BufferedWriter(new FileWriter("output.txt")));
    }
    public HumongusTree(String JUDGE) {
        sc = new FastReader(System.in);
        out = new PrintWriter(System.out);      
    }
    
    String ns() { return sc.next(); }
    int ni() { return sc.nextInt(); }
    long nl() { return sc.nextLong(); }
    int[] ni(int n) {
        int a[]=new int[n];
        for(int i=0;i<n;a[i++]=ni());
        return a;
    }
    long[] nl(int n) {
        long a[]=new long[n];
        for(int i=0;i<n;a[i++]=nl());
        return a;
    }
    
    int[][] ni(int n,int m) {
        int a[][]=new int[n][m];
        for(int i=0;i<n;i++) 
            for(int j=0;j<m;j++)
                a[i][j]=ni();
        return a;
    }
    long[][] nl(int n,int m) {
        long a[][]=new long[n][m];
        for(int i=0;i<n;i++) 
            for(int j=0;j<m;j++)
                a[i][j]=nl();
        return a;
    }
    int gcd(int a, int b) {
        return b==0?a:gcd(b,a%b);
    }
    static class FastReader {
        private InputStream stream;
        private byte[] buf = new byte[1024];
        private int curChar;
        private int numChars;
        private FastReader.SpaceCharFilter filter;
        public FastReader(InputStream stream) {
            this.stream = stream;
        }

        public int read() {
            if (numChars == -1) throw new InputMismatchException();
            if (curChar >= numChars) {
                curChar = 0;
                try {
                    numChars = stream.read(buf);
                } catch (IOException e) {
                    throw new InputMismatchException();
                }
                if (numChars <= 0) return -1;
            }
            return buf[curChar++];
        }

        public int nextInt() {
            int c = read();
            while (isSpaceChar(c)) c = read();
            int sgn = 1;
            if (c == '-') {
                sgn = -1;
                c = read();
            }
            int res = 0;
            do {
                if (c < '0' || c > '9') throw new InputMismatchException();
                res *= 10;
                res += c - '0';
                c = read();
            }
            while (!isSpaceChar(c));
            return res * sgn;
        }
        
        public long nextLong() {
            int c = read();
            while (isSpaceChar(c)) c = read();
            int sgn = 1;
            if (c == '-') {
                sgn = -1;
                c = read();
            }
            long res = 0;
            do {
                if (c < '0' || c > '9') throw new InputMismatchException();
                res = res*1L*10;
                res += c - '0';
                c = read();
            }
            while (!isSpaceChar(c));
            return res *1L* sgn;
        }
        
        public String next() {
            int c = read();
            while (isSpaceChar(c)) c = read();
            StringBuilder res = new StringBuilder();
            do {
                res.appendCodePoint(c);
                c = read();
            } while (!isSpaceChar(c));
            return res.toString();
        }

        public boolean isSpaceChar(int c) {
            if (filter != null) return filter.isSpaceChar(c);
            return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
        }

        public interface SpaceCharFilter {
            public boolean isSpaceChar(int ch);

        }
    }
}