Problem: We have a tree with N vertices. The vertices are numbered 1 to N, and the i-th edge connects Vertex a_i and Vertex b_i.

Takahashi loves the number 3. He is seeking a permutation p_1, p_2, \ldots , p_N of integers from 1 to N satisfying the following condition:

* For every pair of vertices (i, j), if the distance between Vertex i and Vertex j is 3, the sum or product of p_i and p_j is a multiple of 3.



Here the distance between Vertex i and Vertex j is the number of edges contained in the shortest path from Vertex i to Vertex j.

Help Takahashi by finding a permutation that satisfies the condition.

Constraints

* 2\leq N\leq 2\times 10^5
* 1\leq a_i, b_i \leq N
* 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

If no permutation satisfies the condition, print `-1`.

Otherwise, print a permutation satisfying the condition, with space in between. If there are multiple solutions, you can print any of them.

Example

Input

5
1 2
1 3
3 4
3 5


Output

1 2 5 4 3

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
#define ll long long
#define rep(i,l,r) for(int (i)=(l);(i)<(r);(i)++)
#define MAX 200010
#define pb push_back 
using namespace std;

vector<int> v[MAX],ans(MAX);
queue <int> vb,vw;

void dfs(int w,int u,int d){
	if(d%2) vw.push(w);
	else vb.push(w);
	rep(i,0,(int)v[w].size()){
		int to=v[w][i];
        // to avoid return
		if(to!=u) dfs(to,w,d+1);
	}
}

int main(){
	int n;
	cin>>n;
	rep(i,0,n-1){
		int a,b;
		cin>>a>>b;
        a--,b--;
		v[a].pb(b);
		v[b].pb(a);
	}
	dfs(0,-1,0);
    
	if(vb.size()<vw.size()) swap(vb,vw);
	rep(i,1,n+1){
		if(i%3==1){
			int u=vb.front();vb.pop();
			ans[u]=i;
		}
	}
    
	if(vb.size()<vw.size()) swap(vb,vw);
	rep(i,1,n+1){
		if(i%3==2){
			int u=vb.front();vb.pop();
			ans[u]=i;  
		}
	}
    
	rep(i,1,n+1){
		if(i%3==0){
			int u;
			if(!vb.empty()){u=vb.front();vb.pop();}
			else {u=vw.front();vw.pop();}
			ans[u]=i;
		}
	}
	rep(i,0,n) cout<<ans[i]<<" ";
    puts("");
}