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:
/*
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*/

#include <bits/stdc++.h>
//#pragma GCC optimize("O3")
//#pragma GCC optimize("unroll-loops")
#pragma clang diagnostic push
#pragma clang diagnostic ignored "-Wunused-const-variable"
#define popcnt(x) __builtin_popcount(x)

#define fr first

#define sc second

#define m_p make_pair

#define low_bo(a, x) (lower_bound(a.begin(), a.end(), x) - a.begin())

#define up_bo(a, x) (upper_bound(a.begin(), a.end(), x) - a.begin())

#define unique(a) a.resize(unique(a.begin(), a.end()) - a.begin())

#define popcnt(x) __builtin_popcount(x)

#define shuffle(a) shuffle(a.begin(), a.end(), rnd)

//#include <ext/pb_ds/assoc_container.hpp>

//using namespace __gnu_pbds;

//gp_hash_table<int, int> table;

//#pragma GCC optimize("O3")
//#pragma GCC optimize("Ofast,no-stack-protector")
//#pragma GCC target("sse,sse2,sse3,ssse3,sse4,popcnt,abm,mmx")
//#pragma GCC target("avx,tune=native")
//float __attribute__((aligned(32)))

/*char memory[(int)1e8];

char memorypos;

inline void * operator new(size_t n){
    char * ret = memory + memorypos;
    memorypos += n;
    return (void *)ret;
}

inline void operator delete(void *){}
*/

using namespace std;

typedef long long ll;

typedef unsigned long long ull;

//typedef long double ld;

typedef unsigned int uint;

template<typename T>
class Modular {
public:
    using Type = typename decay<decltype(T::value)>::type;

    // 10^9 + 7
    static uint32_t barret;
    static uint32_t kbarret;
    // 998244353


    constexpr Modular() : value() {}

    template<typename U>
    Modular(const U &x) {
        value = normalize(x);
    }

    static Type inverse(Type a, Type mod) {
        Type b = mod, x = 0, y = 1;
        while (a != 0) {
            Type t = b / a;
            b -= a * t;
            x -= t * y;
            swap(a, b);
            swap(x, y);
        }
        if (x < 0)
            x += mod;
        return x;
    }

    template<typename U>
    static Type normalize(const U &x) {
        Type v;
        if ((x >= 0 || -mod() <= x) && x < mod()) v = static_cast<Type>(x);
        else v = static_cast<Type>(x % mod());
        if (v < 0) v += mod();
        return v;
    }

    const Type &operator()() const { return value; }

    template<typename U>
    explicit operator U() const { return static_cast<U>(value); }

    constexpr static Type mod() { return T::value; }

    Modular &operator+=(const Modular &other) {
        if ((value += other.value) >= mod()) value -= mod();
        return *this;
    }

    Modular &operator-=(const Modular &other) {
        if ((value -= other.value) < 0) value += mod();
        return *this;
    }

    template<typename U>
    Modular &operator+=(const U &other) { return *this += Modular(other); }

    template<typename U>
    Modular &operator-=(const U &other) { return *this -= Modular(other); }

    Modular &operator++() { return *this += 1; }

    Modular &operator--() { return *this -= 1; }

    Modular operator++(int) {
        Modular result(*this);
        *this += 1;
        return result;
    }

    Modular operator--(int) {
        Modular result(*this);
        *this -= 1;
        return result;
    }

    Modular operator-() const { return Modular(-value); }

    template<typename U = T>
    typename enable_if<is_same<typename Modular<U>::Type, int>::value, Modular>::type &operator*=(const Modular &rhs) {
/*        int64_t cur = value * (int64_t)rhs.value;
        value = cur - ((cur * (__int128)Modular::barret) >> Modular::kbarret) * mod();
        if (value >= mod())
            value -= mod();
        return *this;*/

#ifdef _WIN32
        uint64_t x = static_cast<int64_t>(value) * static_cast<int64_t>(rhs.value);
        uint32_t xh = static_cast<uint32_t>(x >> 32), xl = static_cast<uint32_t>(x), d, m;
        asm(
        "divl %4; \n\t"
        : "=a" (d), "=d" (m)
        : "d" (xh), "a" (xl), "r" (mod())
        );
        value = m;
#else
        value = normalize(static_cast<int64_t>(value) * static_cast<int64_t>(rhs.value));
#endif
        return *this;

    }

    template<typename U = T>
    typename enable_if<is_same<typename Modular<U>::Type, int64_t>::value, Modular>::type &
    operator*=(const Modular &rhs) {
        int64_t q = static_cast<int64_t>(static_cast<long double>(value) * rhs.value / mod());
        value = normalize(value * rhs.value - q * mod());
        return *this;
    }

    Modular &operator/=(const Modular &other) { return *this *= Modular(inverse(other.value, mod())); }

    //template <typename U>
    //friend const Modular<U>& abs(const Modular<U>& v) { return v; }

    template<typename U>
    friend bool operator==(const Modular<U> &lhs, const Modular<U> &rhs);

    template<typename U>
    friend bool operator<(const Modular<U> &lhs, const Modular<U> &rhs);

    template<typename U>
    friend std::istream &operator>>(std::istream &stream, Modular<U> &number);

private:
    Type value;
};

template<typename T>
bool operator==(const Modular<T> &lhs, const Modular<T> &rhs) { return lhs.value == rhs.value; }

template<typename T, typename U>
bool operator==(const Modular<T> &lhs, U rhs) { return lhs == Modular<T>(rhs); }

template<typename T, typename U>
bool operator==(U lhs, const Modular<T> &rhs) { return Modular<T>(lhs) == rhs; }

template<typename T>
bool operator!=(const Modular<T> &lhs, const Modular<T> &rhs) { return !(lhs == rhs); }

template<typename T, typename U>
bool operator!=(const Modular<T> &lhs, U rhs) { return !(lhs == rhs); }

template<typename T, typename U>
bool operator!=(U lhs, const Modular<T> &rhs) { return !(lhs == rhs); }

template<typename T>
bool operator<(const Modular<T> &lhs, const Modular<T> &rhs) { return lhs.value < rhs.value; }

template<typename T>
Modular<T> operator+(const Modular<T> &lhs, const Modular<T> &rhs) { return Modular<T>(lhs) += rhs; }

template<typename T, typename U>
Modular<T> operator+(const Modular<T> &lhs, U rhs) { return Modular<T>(lhs) += rhs; }

template<typename T, typename U>
Modular<T> operator+(U lhs, const Modular<T> &rhs) { return Modular<T>(lhs) += rhs; }

template<typename T>
Modular<T> operator-(const Modular<T> &lhs, const Modular<T> &rhs) { return Modular<T>(lhs) -= rhs; }

template<typename T, typename U>
Modular<T> operator-(const Modular<T> &lhs, U rhs) { return Modular<T>(lhs) -= rhs; }

template<typename T, typename U>
Modular<T> operator-(U lhs, const Modular<T> &rhs) { return Modular<T>(lhs) -= rhs; }

template<typename T>
Modular<T> operator*(const Modular<T> &lhs, const Modular<T> &rhs) { return Modular<T>(lhs) *= rhs; }

template<typename T, typename U>
Modular<T> operator*(const Modular<T> &lhs, U rhs) { return Modular<T>(lhs) *= rhs; }

template<typename T, typename U>
Modular<T> operator*(U lhs, const Modular<T> &rhs) { return Modular<T>(lhs) *= rhs; }

template<typename T>
Modular<T> operator/(const Modular<T> &lhs, const Modular<T> &rhs) { return Modular<T>(lhs) /= rhs; }

template<typename T, typename U>
Modular<T> operator/(const Modular<T> &lhs, U rhs) { return Modular<T>(lhs) /= rhs; }

template<typename T, typename U>
Modular<T> operator/(U lhs, const Modular<T> &rhs) { return Modular<T>(lhs) /= rhs; }

template<typename T, typename U>
Modular<T> power(const Modular<T> &a, const U &b) {
    assert(b >= 0);
    Modular<T> x = a, res = 1;
    U p = b;
    while (p > 0) {
        if (p & 1) res *= x;
        x *= x;
        p >>= 1;
    }
    return res;
}

template<typename T>
bool IsZero(const Modular<T> &number) {
    return number() == 0;
}

template<typename T>
string to_string(const Modular<T> &number) {
    return to_string(number());
}

template<typename T>
std::ostream &operator<<(std::ostream &stream, const Modular<T> &number) {
    return stream << number();
}

template<typename T>
std::istream &operator>>(std::istream &stream, Modular<T> &number) {
    typename common_type<typename Modular<T>::Type, int64_t>::type x = nullptr;
    stream >> x;
    number.value = Modular<T>::normalize(x);
    return stream;
}


const int md = 1e9 + 7;

using Mint = Modular<std::integral_constant<int, md>>;
template<> uint32_t Mint::barret = 0;
template<> uint32_t Mint::kbarret = 0;

void calc_barret() {
    int k = 0;
    while ((1ll << k) <= md)
        k++;
    Mint::kbarret = k * 2;
    Mint::barret = (1ll << (2 * k)) / md;
}

//#include <atcoder/modint>
//using mint = atcoder::modint998244353;

ll sqr(ll x) {
    return x * x;
}

int mysqrt(ll x) {
    int l = 0, r = 1e9 + 1;
    while (r - l > 1) {
        int m = (l + r) / 2;
        if (m * (ll) m <= x)
            l = m;
        else
            r = m;
    }
    return l;
}

#ifdef ONPC
mt19937 rnd(23);
mt19937_64 rndll(231);
#else
mt19937 rnd(chrono::high_resolution_clock::now().time_since_epoch().count());
    mt19937_64 rndll(chrono::high_resolution_clock::now().time_since_epoch().count());
#endif

template<typename T>
T gcd(T a, T b) {
    return a ? gcd(b % a, a) : b;
}

int gcdex(int a, int b, int &x, int &y) {
    if (a == 0) {
        x = 0;
        y = 1;
        return b;
    }
    int x1, y1;
    int ret = gcdex(b % a, a, x1, y1);
    x = y1 - (b / a) * x1;
    y = x1;
    return ret;
}

void setmin(int &x, int y) {
    x = min(x, y);
}

void setmax(int &x, int y) {
    x = max(x, y);
}

void setmin(ll &x, ll y) {
    x = min(x, y);
}

void setmax(ll &x, ll y) {
    x = max(x, y);
}

const ll llinf = 2e18 + 100;

//#define ld double

const double eps = 1e-12;

const int maxn = 2e5 + 100, maxw = 7 * maxn, inf = 2e9 + 100, sq = 450, LG = 20, mod1 = 1e9 + 993;

int dp(int a, int b, int c, int d) {
    ll w = a * (ll) c + b * (ll)d;
    if (w > 0)
        return 1;
    if (w == 0)
        return 0;
    return -1;
}

pair<int, int> pt[maxn];

pair<int, int> dif(pair<int, int> a, pair<int, int> b) {
    return {b.fr - a.fr, b.sc - a.sc};
}

bool les(int a, int b, int c) {
    auto x = dif(pt[b], pt[a]), y = dif(pt[b], pt[c]);
    return dp(x.fr, x.sc, y.fr, y.sc) > 0;
}

bool check(vector<int> a) {
    for (int i = 1; i + 1 < a.size(); i++)
        if (!les(a[i - 1], a[i], a[i + 1]))
            return 0;
    return 1;
}

int n;

int p[maxn];

int rem[maxn];

bool found;

void go(int it) {
    if (it == n) {
        for (int i = 0; i < n; i++)
            cout << p[i] + 1 << ' ';
        exit(0);
    }
    for (int i = 0; i < 5; i++) {
        int pos = rnd() % (n - it);
        //swap(rem[pos], rem[n - it - 1]);
        if (it > 1 && !les(p[it - 2], p[it - 1], rem[pos])) {
        } else {
            p[it] = rem[pos];
            swap(rem[pos], rem[n - it - 1]);
            go(it + 1);
            swap(rem[pos], rem[n - it - 1]);
            //break;
        }
    }
}

void solve() {
    clock_t st = clock();
    n = 5e3;
    cin >> n;
    for (int i = 0; i < n; i++) {
        rem[i] = i;
        pt[i].fr = 0;
        pt[i].sc = i;
        cin >> pt[i].fr >> pt[i].sc;
    }
    go(0);
    //while ((clock() - st) / (double)CLOCKS_PER_SEC <= 1.5) {
    /*while (1) {
        vector<int> p(n);
        iota(p.begin(), p.end(), 0);
        for (int i = 0; i < n; i++)
            swap(p[i], p[rnd() % (i + 1)]);
        if (check(p)) {
            for (int i : p)
                cout << i + 1 << ' ';
            return;
        }
    }
    cout << -1;*/
}

int main() {
#ifdef ONPC
    freopen("../a.in", "r", stdin);
    freopen("../a.out", "w", stdout);
#else
    //freopen("input.txt", "r", stdin);
    //freopen("output.txt", "w", stdout);
#endif // ONPC
    ios::sync_with_stdio(0);
    cin.tie(0);
    cout.tie(0);
    cout.precision(20);
    cout << fixed;

    if (false) {
        int te = 0;
        while (1) {
            te++;
            cerr << te << '\n';
            solve();
        }
    }
    int t;
    t = 1;
    //cin >> t;
    while (t--) {
        solve();
    }
}