For problem statement at 0-999/500-599/570-579/573/problemC.txt this is a correct solution, but verifier at 0-999/500-599/570-579/573/verifierC.go ends with All 120 tests passed can you fix the verifier? ```go
package main

import (
	"bufio"
	"fmt"
	"os"
)

type FastScanner struct {
	r *bufio.Reader
}

func NewFastScanner() *FastScanner {
	return &FastScanner{r: bufio.NewReader(os.Stdin)}
}

func (fs *FastScanner) nextInt() int {
	sign := 1
	val := 0
	c, _ := fs.r.ReadByte()
	for (c < '0' || c > '9') && c != '-' {
		c, _ = fs.r.ReadByte()
	}
	if c == '-' {
		sign = -1
		c, _ = fs.r.ReadByte()
	}
	for c >= '0' && c <= '9' {
		val = val*10 + int(c-'0')
		c, _ = fs.r.ReadByte()
	}
	return sign * val
}

func main() {
	fs := NewFastScanner()
	n := fs.nextInt()
	g := make([][]int, n)
	deg := make([]int, n)
	for i := 0; i < n-1; i++ {
		a := fs.nextInt() - 1
		b := fs.nextInt() - 1
		g[a] = append(g[a], b)
		g[b] = append(g[b], a)
		deg[a]++
		deg[b]++
	}
	if n <= 2 {
		fmt.Println("Yes")
		return
	}
	inS := make([]bool, n)
	countS := 0
	for i := 0; i < n; i++ {
		if deg[i] > 1 {
			inS[i] = true
			countS++
		}
	}
	if countS == 0 {
		fmt.Println("Yes")
		return
	}
	degS := make([]int, n)
	for v := 0; v < n; v++ {
		if !inS[v] {
			continue
		}
		for _, u := range g[v] {
			if inS[u] {
				degS[v]++
			}
		}
		if degS[v] > 2 {
			fmt.Println("No")
			return
		}
	}
	// check connectivity within S
	visited := make([]bool, n)
	var start int = -1
	for i := 0; i < n; i++ {
		if inS[i] {
			start = i
			break
		}
	}
	stack := make([]int, 0, countS)
	stack = append(stack, start)
	visited[start] = true
	seen := 1
	for len(stack) > 0 {
		v := stack[len(stack)-1]
		stack = stack[:len(stack)-1]
		for _, u := range g[v] {
			if inS[u] && !visited[u] {
				visited[u] = true
				seen++
				stack = append(stack, u)
			}
		}
	}
	if seen != countS {
		fmt.Println("No")
		return
	}
	fmt.Println("Yes")
}
```