import java.io.BufferedReader import java.io.InputStream import java.io.InputStreamReader import java.util.* import kotlin.math.abs import kotlin.math.max import kotlin.math.min val MOD = 1_000_000_007L /** * (dist, parent, queue) */ fun traceBfs(g: Array, rt: Int = 0): Array { val n = g.size val q = IntArray(n) val d = IntArray(n) val p = IntArray(n){-2} var cur = 0 var last = 1 p[rt] = -1 q[0] = rt d[rt] = 0 while (cur < last) { val v = q[cur++] for (u in g[v]) { if (p[u] == -2) { p[u] = v q[last++] = u d[u] = d[v] + 1 } } } return arrayOf(d, p, q) } fun packUGraph(n: Int, from: IntArray, to: IntArray): Array { val p = IntArray(n) val m = from.size for (i in 0 until m) { ++p[from[i]] ++p[to[i]] } val g = Array(n){IntArray(p[it])} for (i in 0 until m) { g[from[i]][--p[from[i]]] = to[i] g[to[i]][--p[to[i]]] = from[i] } return g } class Solver(stream: InputStream, private val out: java.io.PrintWriter) { fun solve() { val N = ni() val (from, to) = na2(N - 1, -1) val g = packUGraph(N, from, to) val (_, par, que) = traceBfs(g) val pow2 = LongArray(N + 1) pow2[0] = 1 for (i in 1 until pow2.size) { pow2[i] = pow2[i - 1] * 2 % MOD } var ans = 0L val dpc = IntArray(N){1} val dp = Array(4){LongArray(N){1} } for (i in N - 1 downTo 0) { val u = que[i] for (v in g[u]) { if (v == par[u]) continue dp[3][u] = dp[3][u] * dp[0][v] % MOD + dp[3][v] * dp[0][u] % MOD + 3 * dp[2][v] * dp[1][u] % MOD + 3 * dp[2][u] * dp[1][v] % MOD + dp[3][u] * dp[0][v] % MOD dp[3][u] %= MOD dp[2][u] = dp[2][u] * dp[0][v] % MOD + dp[2][v] * dp[0][u] % MOD + 2 * dp[1][v] * dp[1][u] % MOD + dp[2][u] * dp[0][v] % MOD dp[2][u] %= MOD dp[1][u] = dp[1][u] * dp[0][v] % MOD + dp[1][v] * dp[0][u] % MOD + dp[1][u] * dp[0][v] % MOD dp[1][u] %= MOD dp[0][u] = dp[0][u] * dp[0][v] * 2 % MOD dpc[u] += dpc[v] debug{"$u->$v"} } debug{"$u"} debugDim(dp) val outNodes = N - dpc[u] ans = (ans + dp[3][u] * pow2[max(0, outNodes - 1)]) % MOD } out.println(ans) } private val isDebug = try { // なんか本番でエラーでる System.getenv("MY_DEBUG") != null } catch (t: Throwable) { false } private var tokenizer: StringTokenizer? = null private val reader = BufferedReader(InputStreamReader(stream), 32768) private fun next(): String { while (tokenizer == null || !tokenizer!!.hasMoreTokens()) { tokenizer = StringTokenizer(reader.readLine()) } return tokenizer!!.nextToken() } private fun ni() = next().toInt() private fun nl() = next().toLong() private fun ns() = next() private fun na(n: Int, offset: Int = 0): IntArray { return map(n) { ni() + offset } } private fun nal(n: Int, offset: Int = 0): LongArray { val res = LongArray(n) for (i in 0 until n) { res[i] = nl() + offset } return res } private fun na2(n: Int, offset: Int = 0): Array { val a = Array(2){IntArray(n)} for (i in 0 until n) { for (e in a) { e[i] = ni() + offset } } return a } private inline fun map(n: Int, f: (Int) -> Int): IntArray { val res = IntArray(n) for (i in 0 until n) { res[i] = f(i) } return res } private inline fun debug(msg: () -> String) { if (isDebug) System.err.println(msg()) } private fun debug(a: LongArray) { debug { a.joinToString(" ") } } private fun debug(a: IntArray) { debug { a.joinToString(" ") } } private fun debug(a: BooleanArray) { debug { a.map { if (it) 1 else 0 }.joinToString("") } } private fun debugDim(A: Array) { if (isDebug) { for (a in A) { debug(a) } } } private fun debugDim(A: Array) { if (isDebug) { for (a in A) { debug(a) } } } /** * 勝手にimport消されるのを防ぎたい */ private fun hoge() { min(1, 2) max(1, 2) abs(-10) } } fun main() { val out = java.io.PrintWriter(System.out) Solver(System.`in`, out).solve() out.flush() }