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 C++14 (GCC 5.4.1) (judge verdict: Wrong Answer)


#include <stdio.h>
#include <iostream>
#include <string.h>
#include <limits.h>
#include <string>
#include <vector>
#include <algorithm>
#include <map>
#include <set>

typedef unsigned long long ULLONG;
typedef long long LLONG;

template <class _T> static _T tp_abs(const _T& a) {
	return ((a < 0) ? (a * -1) : a);
}
template <class _T> static _T tp_min(_T a, _T b) {
	return a < b ? a : b;
}
template <class _T> static _T tp_max(_T a, _T b) {
	return a > b ? a : b;
}
template<class _T> static void get1int(_T& a) {
	const char* fmt = " %d";
	if (sizeof(_T) == sizeof(long long)) {
		fmt = " %lld";
	}

	if (scanf(fmt, &a) < 0) {
		printf("g1int Error\n");
	}
}
template<class _T> static void get2int(_T& a, _T& b) {
	const char* fmt = " %d %d";
	if (sizeof(_T) == sizeof(long long)) {
		fmt = " %lld %lld";
	}

	if (scanf(fmt, &a, &b) < 0) {
		printf("g2int Error\n");
	}
}
template<class _T> static void get3int(_T& a, _T& b, _T& c) {
	const char* fmt = " %d %d %d";
	if (sizeof(_T) == sizeof(long long)) {
		fmt = " %lld %lld %lld";
	}

	if (scanf(fmt, &a, &b, &c) < 0) {
		printf("g3int Error\n");
	}
}
static void getstring(char* buff) {
	if (scanf(" %s", buff) < 0) {
		printf("getstr error!\n");
	}
}

static const long long MOD_NUM = 1000000007LL;

static void D_task();

int main()
{
	D_task();
	fflush(stdout);
	return 0;
}

class D_edge {
public:
	int to = 0;
	int eNo = 0;
};

static void D_task()
{
	int N;
	get1int(N);

	std::vector<std::vector<D_edge>> graph(N);

	for (int i = 0; i < N - 1; i++) {
		int a, b;
		get2int(a, b); a--; b--;
		D_edge e;
		e.eNo = i;
		e.to = b;
		graph[a].push_back(e);
		e.to = a;
		graph[b].push_back(e);
	}

	int colorCnt = 0;
	for (int i = 0; i < N; i++) {
		colorCnt = tp_max(colorCnt, (int)graph[i].size());
	}

	std::vector<int> eColor(N - 1, 0);
	for (int i = 0; i < N; i++) {
		std::set<int> used;
		
		int eCnt = graph[i].size();
		int color = 1;
		for (int e = 0; e < eCnt; e++) {
			int eNo = graph[i][e].eNo;
			if (eColor[eNo] == 0) {
				while (used.find(color) != used.end()) {
					color++;
				}
				eColor[eNo] = color;
			}
			used.insert(eColor[eNo]);
		}
//		used.clear();
	}
	
	printf("%d\n", colorCnt);
	for (int i = 0; i < N - 1; i++) {
		printf("%d\n", eColor[i]);
	}
}