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>
using namespace std;
#define rep(i,n) for(int i=0; i<(n); i++)
int n, v, u, p[200005], e[2], m[2][200005], mi;
vector<int> G[200005];

void dfs(int u, int p, int d){
	m[d][e[d]++] = u;
	for(int nx: G[u]) if(nx != p) dfs(nx, u, d^1);
}
int main(){
	scanf("%d", &n);
	rep(i,n-1){
		scanf("%d%d", &v, &u);
		v--; u--;
		G[v].push_back(u);
		G[u].push_back(v);
	}
	dfs(0,0,0);
	mi = e[0] > e[1];
	if(e[mi] <= n/3){
		rep(i,e[mi]) p[m[mi][i]] = (i+1)*3;
		rep(i,e[mi^1]) p[m[mi^1][i]] = (i+e[mi]-n/3 < 0 ? (i+1+e[mi])*3 : (i+e[mi]-n/3) < (n+2)/3 ? (i+e[mi]-n/3)*3 + 1 : (i+e[mi]-n/3-(n+2)/3)*3+2);
	}else{
		rep(i,e[0]) p[m[0][i]] = i<(n+1)/3 ? i*3+2 : (i-(n+1)/3+1)*3;
		rep(i,e[1]) p[m[1][i]] = i<(n+2)/3 ? i*3+1 : (i+e[0]-(n+1)/3-(n+2)/3+1)*3;
	}
	rep(i,n) printf("%d%c", p[i], i==n-1 ? '\n' : ' ');
}