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: Runtime Error)

#include "bits/stdc++.h"
using namespace std;

#define ASC(vec) vec.begin(), vec.end()		// 昇順ソート 例：sort(ASC(vec));
#define DESC(vec) vec.rbegin(), vec.rend()	// 降順ソート 例:sort(DESC(vec));
#define rep(i, n) for(int i = 0; i < n; i++)
#define Rep(i, n) for(int i = 1; i < n; i++)

const int mod = 1000000007;
const int inf = (int)1e9 + 7;
const long long INF = 1LL << 60;

using ii = pair<int, int>;
using ll = long long;
using vi = vector<int>;
using vd = vector<double>;
using vb = vector<bool>;
using vl = vector<ll>;
using vs = vector<string>;
using vvi = vector<vector<int>>;
using vvl = vector<vector<ll>>;
using vii = vector<pair<int, int>>;

template<class T> inline bool chmin(T& a, T b) { if (a > b) { a = b; return true; } return false; }
template<class T> inline bool chmax(T& a, T b) { if (a < b) { a = b; return true; } return false; }

ll GCD(ll a, ll b) { return b ? GCD(b, a % b) : a; }
ll LCM(ll a, ll b) { return (a * b) / GCD(a, b); }
int round_int(int a, int b) { return (a + (b - 1)) / b; }

// 素因数分解; 返り値は(素数, 乗数)のvector配列
vector<pair<ll, int>> factorize(ll n) {
	vector<pair<ll, int>> res;
	for (ll i = 2; i * i <= n; ++i) {
		if (n % i) continue;
		res.emplace_back(i, 0);
		while (n % i == 0) {
			n /= i;
			res.back().second++;
		}
	}
	if (n != 1) res.emplace_back(n, 1);
	return res;
}

constexpr array<int, 9> dx = { 0, 1, 0, -1, -1, 1, 1, -1, 0 };
constexpr array<int, 9> dy = { 1, 0, -1, 0, 1, 1, -1, -1, 0 };
constexpr auto MAX = 100010;

// ──────────────────────────────────────────────────────────────────────────────

struct Edge
{
	int to;
	int id;
};

vector<vector<Edge>> g;
vi ans;

void dfs(int v, int c = -1, int p = -1) {
	int k = 1;
	for (int i = 0; i < g[v].size(); ++i) {
		int u = g[v][i].to, ei = g[v][i].id;
		if (u == p) continue;
		if (k == c) ++k;
		ans[ei] = k; 
		++k;
		dfs(u, ans[ei], v);
	}
}

int main() {
	int n;
	cin >> n;
	g.resize(n);

	rep(i, n - 1) {
		int a, b;
		cin >> a >> b;
		--a, --b;
		Edge edge1 = { b, i };
		Edge edge2 = { a, i };
	}
	dfs(0);

	int mx = 0;
	rep(i, n) mx = max(mx, int(g[i].size()));
	cout << mx << endl;
	rep(i, n - 1) {
		cout << ans[i] << endl;
	}
}