Problem:
Score : 400 points

Problem Statement

Given is a tree G with N vertices.
The vertices are numbered 1 through N, and the i-th edge connects Vertex a_i and Vertex b_i.

Consider painting the edges in G with some number of colors.
We want to paint them so that, for each vertex, the colors of the edges incident to that vertex are all different.

Among the colorings satisfying the condition above, construct one that uses the minimum number of colors.

Constraints

2 \le N \le 10^5

1 \le a_i \lt b_i \le N

All values in input are integers.

The given graph is a tree.

Input

Input is given from Standard Input in the following format:

N
a_1 b_1
a_2 b_2
\vdots
a_{N-1} b_{N-1}

Output

Print N lines.

The first line should contain K, the number of colors used.

The (i+1)-th line (1 \le i \le N-1) should contain c_i, the integer representing the color of the i-th edge, where 1 \le c_i \le K must hold.

If there are multiple colorings with the minimum number of colors that satisfy the condition, printing any of them will be accepted.

Sample Input 1

3
1 2
2 3

Sample Output 1

2
1
2

Sample Input 2

8
1 2
2 3
2 4
2 5
4 7
5 6
6 8

Sample Output 2

4
1
2
3
4
1
1
2

Sample Input 3

6
1 2
1 3
1 4
1 5
1 6

Sample Output 3

5
1
2
3
4
5

Solution in Go (1.6) (judge verdict: Accepted)

package main

import (
	"bufio"
	"fmt"
	"io"
	"log"
	"os"
	"strconv"
)

type Edge struct {
	to   int
	outi int
}

var mat [][]Edge
var visited []bool
var ans []int
var k int

func dfs(cur, color int) {
	visited[cur] = true

	nexts := mat[cur]
	i, nxcolor := 0, 1
	for i < len(nexts) {
		if visited[nexts[i].to] {
			i++
			continue
		}
		if nxcolor == color {
			nxcolor++
			continue
		}

		dfs(nexts[i].to, nxcolor)

		k = max(k, nxcolor)
		ans[nexts[i].outi] = nxcolor

		i++
		nxcolor++
	}
}

func main() {
	n := readInt()

	mat = make([][]Edge, n)
	for i := range mat {
		mat[i] = make([]Edge, 0)
	}

	for i := 0; i < n-1; i++ {
		a, b := readInt()-1, readInt()-1
		mat[a] = append(mat[a], Edge{b, i})
		mat[b] = append(mat[b], Edge{a, i})
	}

	ans = make([]int, n-1)
	visited = make([]bool, n)

	dfs(0, -1)

	fmt.Println(k)
	for i := range ans {
		fmt.Println(ans[i])
	}
}

// sort ------------------------------------------------------------

type xxx struct {
	x int
}

type sortArray []xxx

func (s sortArray) Len() int           { return len(s) }
func (s sortArray) Swap(i, j int)      { s[i], s[j] = s[j], s[i] }
func (s sortArray) Less(i, j int) bool { return s[i].x < s[j].x }

// -----------------------------------------------------------------

var (
	readString func() string
	readBytes  func() []byte
)

func init() {
	log.SetFlags(log.Lshortfile)
	readString, readBytes = newReadString(os.Stdin)
}

func newReadString(ior io.Reader) (func() string, func() []byte) {
	r := bufio.NewScanner(ior)
	r.Buffer(make([]byte, 1024), int(1e+11))
	r.Split(bufio.ScanWords)

	f1 := func() string {
		if !r.Scan() {
			panic("Scan failed")
		}
		return r.Text()
	}
	f2 := func() []byte {
		if !r.Scan() {
			panic("Scan failed")
		}
		return r.Bytes()
	}
	return f1, f2
}

func readInt() int {
	return int(readInt64())
}

func readInt64() int64 {
	i, err := strconv.ParseInt(readString(), 10, 64)
	if err != nil {
		panic(err.Error())
	}
	return i
}

func readFloat64() float64 {
	f, err := strconv.ParseFloat(readString(), 64)
	if err != nil {
		panic(err.Error())
	}
	return f
}

func min(a, b int) int {
	if a < b {
		return a
	}
	return b
}

func max(a, b int) int {
	if a > b {
		return a
	}
	return b
}

func abs(a int) int {
	if a < 0 {
		return -a
	}
	return a
}

func sum(a []int) int {
	var ret int
	for i := range a {
		ret += a[i]
	}
	return ret
}

func sumFloat64(a []float64) float64 {
	var ret float64
	for i := range a {
		ret += a[i]
	}
	return ret
}

func gcd(m, n int) int {
	for m%n != 0 {
		m, n = n, m%n
	}
	return n
}

func lcm(m, n int) int {
	return m / gcd(m, n) * n
}