Problem: Nezzar loves the game osu!.

osu! is played on beatmaps, which can be seen as an array consisting of distinct points on a plane. A beatmap is called nice if for any three consecutive points A,B,C listed in order, the angle between these three points, centered at B, is strictly less than 90 degrees.

<image> Points A,B,C on the left have angle less than 90 degrees, so they can be three consecutive points of a nice beatmap; Points A',B',C' on the right have angle greater or equal to 90 degrees, so they cannot be three consecutive points of a nice beatmap.

Now Nezzar has a beatmap of n distinct points A_1,A_2,…,A_n. Nezzar would like to reorder these n points so that the resulting beatmap is nice.

Formally, you are required to find a permutation p_1,p_2,…,p_n of integers from 1 to n, such that beatmap A_{p_1},A_{p_2},…,A_{p_n} is nice. If it is impossible, you should determine it.

Input

The first line contains a single integer n (3 ≤ n ≤ 5000).

Then n lines follow, i-th of them contains two integers x_i, y_i (-10^9 ≤ x_i, y_i ≤ 10^9) — coordinates of point A_i.

It is guaranteed that all points are distinct.

Output

If there is no solution, print -1.

Otherwise, print n integers, representing a valid permutation p.

If there are multiple possible answers, you can print any.

Example

Input


5
0 0
5 0
4 2
2 1
3 0


Output


1 2 5 3 4

Note

Here is the illustration for the first test:

<image>

Please note that the angle between A_1, A_2 and A_5, centered at A_2, is treated as 0 degrees. However, angle between A_1, A_5 and A_2, centered at A_5, is treated as 180 degrees.

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
#define fio ios_base::sync_with_stdio(0);cin.tie(0);cout.tie(0);
#define ll long long
#define en cin.close();return 0;
#define INF ((ll)(4e18))
#define pb push_back
#define fi first//printf("%lli\n",cur);
#define se second//scanf("%lli",&n);
using namespace std;
const ll N = 5005;
bool use[N];
ll pw2(ll n)
{
    return n*n;
}
int main()
{
    fio
    //ifstream cin("in.inn");
    ll n;
    cin >> n;
    pair<ll,ll> p[n];
    vector<ll> ans;
    for(auto &i:p)
        cin >> i.fi >> i.se;
    ll cur = 0;
    ans.pb(0);
    use[0]=1;
    for(ll i = 1;i<n;i++)
    {
        ll mx = -INF, pos;
        for(ll j = 0;j<n;j++)
        {
            if(!use[j])
            {
                ll dist = pw2(p[j].fi-p[cur].fi)+pw2(p[j].se-p[cur].se);
                if(mx<dist)
                    mx=dist,
                    pos=j;
            }
        }
        use[pos]=1;
        cur=pos;
        ans.pb(cur);
    }
    for(auto i:ans)
        cout << i+1 << " ";
    //cin.close();
    return 0;
}