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: Accepted)

/* monkukui 競技プログラミング用のテンプレート  (ここから) */
#include <iostream>
#include <cstdio>
#include <string>
#include <cstring>
#include <deque>
#include <list>
#include <queue>
#include <stack>
#include <vector>
#include <utility>
#include <algorithm>
#include <map>
#include <set>
#include <complex>
#include <cmath>
#include <limits>
#include <climits>
#include <ctime>
#include <cassert>
#include <numeric>
#include <functional>
#include <bitset>

using namespace std;
using lint = long long int;
using ll = long long int;
using lnt = long long int;
using Graph = vector<vector<int>>;
using Wgraph = vector<vector<pair<int, long long int>>>;
constexpr long long int INF = 1001001001001001LL;
constexpr long long int MOD = 1000000007LL;
constexpr double PI = 3.1415926535897932;
constexpr long long int di[] = {-1, 0, 1, 0, -1, 1, 1, -1};
constexpr long long int dj[] = {0, 1, 0, -1, 1, 1, -1, -1};

template<typename T1,typename T2> inline void chmin(T1 &a,T2 b){if(a>b) a=b;}
template<typename T1,typename T2> inline void chmax(T1 &a,T2 b){if(a<b) a=b;}
inline void yes(){ cout << "yes" << endl; }
inline void Yes(){ cout << "Yes" << endl; }
inline void YES(){ cout << "YES" << endl; }
inline void no(){ cout << "no" << endl; }
inline void No(){ cout << "No" << endl; }
inline void NO(){ cout << "NO" << endl; }
inline void possible(){ cout << "possible" << endl; }
inline void Possible(){ cout << "Possible" << endl; }
inline void POSSIBLE(){ cout << "POSSIBLE" << endl; }
inline void impossible(){ cout << "impossible" << endl; }
inline void Impossible(){ cout << "Impossible" << endl; }
inline void IMPOSSIBLE(){ cout << "IMPOSSIBLE" << endl; }

#define REP(i,n) for(int i = 0; i < (n); i++)
#define RREP(i,n) for(int i = 1; i <= (n); i++)
#define DREP(i,n) for(int i = (n)-1; i >= 0; i--)
#define SREP(i,s,t) for(int i = s; i < t; i++)
#define ALL(a) a.begin(),a.end()
#define RALL(a) a.rbegin(),a.rend()
#define PB push_back

/* monkukui 競技プログラミング用のテンプレート (ここまで)*/
int md;

void dfs(int cur, vector<vector<int>> &g, map<pair<int, int>, int> &color, vector<int> &used, int c) {
  used[cur] = 1;
  for(int i = 0; i < g[cur].size(); i++) {
    int nxt = g[cur][i];
    if(used[nxt] == 1) continue;
    color[{cur, nxt}] = c;
    color[{nxt, cur}] = c;
    c = c + 1;
    c %= md;
    dfs(nxt, g, color, used, c);
  }
}

int main(){
  
  int n; cin >> n;
  vector<vector<int>> g(n);
  vector<int> d(n, 0);
  map<pair<int, int>, int> id;
  for(int i = 0; i < n - 1; i++) {
    int a, b; cin >> a >> b;
    a--;
    b--;
    d[a]++;
    d[b]++;
    g[a].push_back(b);
    g[b].push_back(a);
    id[{a, b}] = i;
    id[{b, a}] = i;
  }

  for(int i = 0; i < n; i++) md = max(md, d[i]);

  map<pair<int, int>, int> color;
  vector<int> used(n, 0);
  dfs(0, g, color, used, 0);
  vector<int> ans(n - 1);
  for(int i = 0; i < n; i++) {
    for(int j = 0; j < g[i].size(); j++) {
      int idd = id[{i, g[i][j]}];
      ans[idd] = color[{i, g[i][j]}];
    }
  }
  
  cout << md << endl;
  for(auto hoge : ans) cout << hoge + 1 << endl;

  return 0;
}