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;

const int MAX_N=2e5+10;

int N,a,b,now=3;
vector<vector<int>> G(MAX_N);
vector<queue<int>> qs(2);
vector<int> dep(MAX_N,0),ans(MAX_N,0);

void dfs(int v,int p){
    qs[dep[v]&1].push(v);
    for (int u:G[v]){
        if (u==p) continue;
        dep[u]=dep[v]+1;
        dfs(u,v);
    }
}

int main(){
    cin.tie(0);
    ios::sync_with_stdio(false);
    cin >> N;
    for (int i=0;i<N-1;++i){
        cin >> a >> b; --a,--b;
        G[a].emplace_back(b);
        G[b].emplace_back(a);
    }
    dfs(0,-1);
    if (qs[0].size()<qs[1].size()) swap(qs[0],qs[1]);
    for (int i=1;i<=N;i+=3){
        ans[qs[0].front()]=i; qs[0].pop();
    }
    if (qs[0].size()<qs[1].size()) swap(qs[0],qs[1]);
    for (int i=2;i<=N;i+=3){
        ans[qs[0].front()]=i; qs[0].pop();
    }
    for (int i=0;i<N;++i) if (!ans[i]){
        ans[i]=now; now+=3;
    }
    for (int i=0;i<N;++i) cout << ans[i] << (i!=N-1?' ':'\n');
}