For problem statement at 1000-1999/1200-1299/1210-1219/1211/problemH.txt this is a correct solution, but verifier at 1000-1999/1200-1299/1210-1219/1211/verifierH.go ends with Test 1 failed
Input:
 1
2
1 2

Expected:
 
Output:
 1
1 can you fix the verifier? ```go
package main

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

type Edge struct {
	to, idx int
}

func main() {
	reader := bufio.NewReader(os.Stdin)
	writer := bufio.NewWriter(os.Stdout)
	defer writer.Flush()

	var t int
	if _, err := fmt.Fscan(reader, &t); err != nil {
		return
	}

	for tc := 0; tc < t; tc++ {
		var n int
		fmt.Fscan(reader, &n)

		adj := make([][]Edge, n+1)
		for i := 1; i < n; i++ {
			var u, v int
			fmt.Fscan(reader, &u, &v)
			adj[u] = append(adj[u], Edge{v, i})
			adj[v] = append(adj[v], Edge{u, i})
		}

		children := make([][]Edge, n+1)
		var buildDirTree func(u, p int)
		buildDirTree = func(u, p int) {
			for _, edge := range adj[u] {
				if edge.to != p {
					children[u] = append(children[u], edge)
					buildDirTree(edge.to, u)
				}
			}
		}
		buildDirTree(1, 0)
		root := 1

		check := func(r int) bool {
			var dfs func(u int) int
			possible := true
			dfs = func(u int) int {
				if !possible {
					return 0
				}
				W := make([]int, len(children[u]))
				sum := 0
				for i, child := range children[u] {
					W[i] = dfs(child.to) + 1
					if !possible {
						return 0
					}
					sum += W[i]
				}

				dp := make([]bool, r+1)
				dp[0] = true
				for _, w := range W {
					for j := r; j >= w; j-- {
						if dp[j-w] {
							dp[j] = true
						}
					}
				}

				maxB := 0
				for j := r; j >= 0; j-- {
					if dp[j] {
						maxB = j
						break
					}
				}

				f_u := sum - maxB
				if u == root {
					if f_u > r {
						possible = false
					}
				} else {
					if f_u > r-1 {
						possible = false
					}
				}
				return f_u
			}
			dfs(root)
			return possible
		}

		left, right := 1, n-1
		ansR := n - 1
		for left <= right {
			mid := (left + right) / 2
			if check(mid) {
				ansR = mid
				right = mid - 1
			} else {
				left = mid + 1
			}
		}

		f := make([]int, n+1)
		inB := make([][]bool, n+1)

		var calcF func(u int)
		calcF = func(u int) {
			k := len(children[u])
			W := make([]int, k)
			for i, child := range children[u] {
				calcF(child.to)
				W[i] = f[child.to] + 1
			}

			dp := make([][]bool, k+1)
			for i := range dp {
				dp[i] = make([]bool, ansR+1)
			}
			dp[0][0] = true

			for i := 0; i < k; i++ {
				w := W[i]
				for j := 0; j <= ansR; j++ {
					if dp[i][j] {
						dp[i+1][j] = true
						if j+w <= ansR {
							dp[i+1][j+w] = true
						}
					}
				}
			}

			maxB := 0
			for j := ansR; j >= 0; j-- {
				if dp[k][j] {
					maxB = j
					break
				}
			}

			sum := 0
			for _, w := range W {
				sum += w
			}
			f[u] = sum - maxB

			in_B := make([]bool, k)
			curr := maxB
			for i := k - 1; i >= 0; i-- {
				w := W[i]
				if dp[i][curr] {
					in_B[i] = false
				} else {
					in_B[i] = true
					curr -= w
				}
			}
			inB[u] = in_B
		}

		calcF(root)

		ans := make([]int, n)
		colorCounter := 0

		var assign func(u int, parent_color int)
		assign = func(u int, parent_color int) {
			var new_color int
			hasB := false
			for i := range children[u] {
				if inB[u][i] {
					hasB = true
					break
				}
			}
			if hasB {
				colorCounter++
				new_color = colorCounter
			}

			for i, child := range children[u] {
				v := child.to
				idx := child.idx
				if inB[u][i] {
					ans[idx] = new_color
					assign(v, new_color)
				} else {
					ans[idx] = parent_color
					assign(v, parent_color)
				}
			}
		}

		assignRoot := func() {
			var colorA, colorB int
			hasA, hasB := false, false
			for i := range children[root] {
				if inB[root][i] {
					hasB = true
				} else {
					hasA = true
				}
			}
			if hasA {
				colorCounter++
				colorA = colorCounter
			}
			if hasB {
				colorCounter++
				colorB = colorCounter
			}

			for i, child := range children[root] {
				v := child.to
				idx := child.idx
				if inB[root][i] {
					ans[idx] = colorB
					assign(v, colorB)
				} else {
					ans[idx] = colorA
					assign(v, colorA)
				}
			}
		}

		assignRoot()

		fmt.Fprintln(writer, ansR)
		for i := 1; i < n; i++ {
			if i > 1 {
				fmt.Fprint(writer, " ")
			}
			fmt.Fprint(writer, ans[i])
		}
		fmt.Fprintln(writer)
	}
}
```