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++ (GCC 9.2.1) (judge verdict: Accepted)

#include <bits/stdc++.h>
using namespace std;
 
 
typedef long long ll;
typedef pair<int,int> ii;
typedef vector<int> vi;
typedef vector<ii> vii;
typedef long double ld;
 
typedef set<int>::iterator sit;
typedef map<int,int>::iterator mit;
typedef vector<int>::iterator vit;
 
const int INF = 1e9 + 7;
const int MOD = 1e9 + 7;
const int MAXN = 1e6 + 3;
 
#define _  %  MOD
#define __ %= MOD
 
#define      each(it,s)        for(auto it = s.begin(); it != s.end(); ++it)
#define      sortA(v)          sort(v.begin(), v.end())
#define      sortD(v)          sort(v.begin(), v.end(), greater<auto>())
#define      fill(a)           memset(a, 0, sizeof (a))
 
#define      swap(a,b)        {a=a+b;b=a-b;a=a-b;}
#define      rep(i, n)         for(ll i = 0; i < (n); ++i)
#define      repA(i, a, n)     for(ll i = a; i <= (n); ++i)
#define      repD(i, a, n)     for(ll i = a; i >= (n); --i)
#define watch(x) cout << (#x) << " is " << (x) <<endl
 
#define fi first
#define se second
#define mp make_pair
#define pb push_back
 
#define fbo find_by_order
#define ook order_of_key
 
ll gcd(ll a,ll b){if(b==0) return a; else return gcd(b,a%b);}
ll power(ll x,ll y){ll res=1; while(y>0){if(y&1) res=res*x;y=y>>1;x=x*x;}return res;} // modular exponent
ll n;
ll ans=0;
const int N=1e5+5;
vector<ll> adj[N];
map<pair<ll,ll>,ll> m;
map<ll,ll> clr;
void dfs(ll u,ll par,ll parcol)
{
	ll childcol=(parcol+1)%ans;
	pair<ll,ll> edge=mp(min(u,par),max(u,par));
	clr[m[edge]]=childcol;
	for(auto v:adj[u])
	{
		if(v==par) continue;
		dfs(v,u,childcol);
		childcol=(childcol+1)%ans;
	}
	return ;
}
int main()
{
    ios_base::sync_with_stdio(false); // don't use printf and scanf
    cin.tie(NULL); // cout<<fixed<<setprecision
	cin>>n;
	m[mp(0ll,1ll)]=0ll;
	repA(i,1,n-1)
	{
		ll x,y;
		cin>>x>>y;
		if(x>y) swap(x,y);
		m[mp(x,y)]=i;
		adj[x].pb(y);
		adj[y].pb(x);
	}
	repA(i,1,n) ans=max(ans,(ll)adj[i].size());
	cout<<ans<<'\n';
	dfs(1,0,-1);
	for(auto it:clr)
	{
		if(it.fi==0) continue;
		cout<<it.se+1<<'\n';
	}
	return 0;
}
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