Given a tree with n nodes numbered from 1 to n. Each node i has an associated value V_i.

If the simple path from u_1 to u_m consists of m nodes namely u_1 → u_2 → u_3 → ... u_{m-1} → u_{m}, then its alternating function A(u_{1},u_{m}) is defined as A(u_{1},u_{m}) = ∑_{i=1}^{m} (-1)^{i+1} ⋅ V_{u_{i}}. A path can also have 0 edges, i.e. u_{1}=u_{m}.

Compute the sum of alternating functions of all unique simple paths. Note that the paths are directed: two paths are considered different if the starting vertices differ or the ending vertices differ. The answer may be large so compute it modulo 10^{9}+7. 

Input

The first line contains an integer n (2 ≤ n ≤ 2⋅10^{5} ) — the number of vertices in the tree.

The second line contains n space-separated integers V_1, V_2, …, V_n (-10^9≤ V_i ≤ 10^9) — values of the nodes.

The next n-1 lines each contain two space-separated integers u and v (1≤ u, v≤ n, u ≠ v) denoting an edge between vertices u and v. It is guaranteed that the given graph is a tree.

Output

Print the total sum of alternating functions of all unique simple paths modulo 10^{9}+7. 

Examples

Input

4
-4 1 5 -2
1 2
1 3
1 4


Output

40


Input

8
-2 6 -4 -4 -9 -3 -7 23
8 2
2 3
1 4
6 5
7 6
4 7
5 8


Output

4

Note

Consider the first example.

A simple path from node 1 to node 2: 1 → 2 has alternating function equal to A(1,2) = 1 ⋅ (-4)+(-1) ⋅ 1 = -5.

A simple path from node 1 to node 3: 1 → 3 has alternating function equal to A(1,3) = 1 ⋅ (-4)+(-1) ⋅ 5 = -9.

A simple path from node 2 to node 4: 2 → 1 → 4 has alternating function A(2,4) = 1 ⋅ (1)+(-1) ⋅ (-4)+1 ⋅ (-2) = 3.

A simple path from node 1 to node 1 has a single node 1, so A(1,1) = 1 ⋅ (-4) = -4.

Similarly, A(2, 1) = 5, A(3, 1) = 9, A(4, 2) = 3, A(1, 4) = -2, A(4, 1) = 2, A(2, 2) = 1, A(3, 3) = 5, A(4, 4) = -2, A(3, 4) = 7, A(4, 3) = 7, A(2, 3) = 10, A(3, 2) = 10. So the answer is (-5) + (-9) + 3 + (-4) + 5 + 9 + 3 + (-2) + 2 + 1 + 5 + (-2) + 7 + 7 + 10 + 10 = 40.

Similarly A(1,4)=-2, A(2,2)=1, A(2,1)=5, A(2,3)=10, A(3,3)=5, A(3,1)=9, A(3,2)=10, A(3,4)=7, A(4,4)=-2, A(4,1)=2, A(4,2)=3 , A(4,3)=7 which sums upto 40. 
import java.io.BufferedOutputStream;
import java.io.BufferedReader;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.LinkedList;
import java.util.StringTokenizer;

public class Round474E {

	public static long mod = (long)1e9+7;
	public static Pair[] dp;
	public static LinkedList<Integer>[] adj;
	public static long[] val;
	
	public static void dfs(int curr, int pr) {
		long sum = 0, ways = 0;
		for(Integer x : adj[curr]) {
			if(x != pr) {
				dfs(x, curr);
				sum += dp[x].sum;
				sum %= mod;
				ways += dp[x].ways;
//				if(sum >= mod) sum -= mod;
				if(sum < 0) sum += mod;
//				if(ways >= mod) ways -= mod;
			}
		}
		ways++;
		sum = ((ways * val[curr])%mod - (sum))%mod;
		if(sum < 0) sum += mod;
		dp[curr] = new Pair(sum, ways);
	}
	
	public static void dfs2(int curr, int pr) {
		if(curr == 0) {
			for(Integer x : adj[curr]) {
				dfs2(x, curr);
			}
		}else {
			long sum = (dp[pr].sum + dp[curr].sum)%mod;
//			if(sum >= mod) sum -= mod;
			if(sum < 0) sum += mod;
			sum = (sum - (val[pr] * dp[curr].ways)%mod)%mod;
			if(sum < 0) sum += mod;
//			if(sum >= mod) sum -= mod;
			long ways = dp[pr].ways - dp[curr].ways;
			dp[curr].sum -= sum;
			dp[curr].sum %= mod;
			if(dp[curr].sum < 0) dp[curr].sum+=mod;
//			if(dp[curr].sum >= mod ) dp[curr].sum -= mod;
			dp[curr].sum += (ways * val[curr])%mod;
			dp[curr].sum %= mod;
//			if(dp[curr].sum >= mod ) dp[curr].sum -= mod;
			if(dp[curr].sum < 0) dp[curr].sum+=mod;
			dp[curr].ways += ways;
			for(Integer x : adj[curr]) {
				if(x != pr) {
					dfs2(x, curr);
				}
			}
		}
	}
	
	public static void solve() {
		int n = s.nextInt();	
		adj = new LinkedList[n]; 
		for(int i = 0; i < n; i++) adj[i] = new LinkedList<Integer>();
		val = new long[n];
		for(int i = 0; i < n; i++) val[i] = s.nextLong();
		for(int i = 0; i < n - 1; i++) {
			int a = s.nextInt() - 1;
			int b = s.nextInt() - 1;
			adj[a].add(b); adj[b].add(a);
		}
		dp = new Pair[n];
		dfs(0, 0);
		dfs2(0, 0);
		long sum = 0;
		for(int i = 0; i < n; i++) {
			sum+= dp[i].sum;
			if(sum >= mod) sum -= mod;
		}
		out.println(sum);
	}

	public static class Pair{
		long sum;
		long ways;
		public Pair(long sum, long ways) {
			this.sum = sum;
			this.ways = ways;
		}
	}
	
	public static void main(String[] args) {
		out = new PrintWriter(new BufferedOutputStream(System.out));
		s = new FastReader();
		solve();
		out.close();
	}

	public static FastReader s;
	public static PrintWriter out;

	public static class FastReader {
		BufferedReader br;
		StringTokenizer st;

		public FastReader() {
			br = new BufferedReader(new InputStreamReader(System.in));
		}

		String next() {
			while (st == null || !st.hasMoreTokens()) {
				try {
					st = new StringTokenizer(br.readLine());
				} catch (Exception e) {
					e.printStackTrace();
				}
			}
			return st.nextToken();
		}

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

		double nextDouble() {
			return Double.parseDouble(next());
		}

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

		String nextLine() {
			String str = "";
			try {
				str = br.readLine();
			} catch (Exception e) {
				e.printStackTrace();
			}
			return str;
		}
	}

	
}
