#include <stdio.h>
#include <stdlib.h>
#include <iostream>
#include <iomanip>
#include <vector>
#include <string.h>
#include <string>
#include <map>
#include <stack>
#include <queue>
#include <deque>
#include <set>
#include <math.h>
#include <algorithm>
#include <numeric>

//using namespace atcoder;
//#include <atcoder/convolution>
//#include <atcoder/lazysegtree>
//#include <atcoder/math>
//#include <atcoder/maxflow>
//#include <atcoder/mincostflow>
//#include <atcoder/modint>
//#include <atcoder/scc>
//#include <atcoder/segtree>
//#include <atcoder/string>
//#include <atcoder/twosat>


using namespace std;

// マクロ&定数&関数 ================================================
typedef unsigned int uint;
typedef long long ll;

typedef pair<ll, ll> pll;
typedef pair<int, int> pint;

typedef vector<int> vint;
typedef vector<ll> vll;
typedef vector<double> vdouble;
typedef vector<bool> vbool;
typedef vector<string> vstring;

typedef vector<pair<int, int>> vpint;
typedef vector<pair<ll, ll>> vpll;
typedef vector<pair<double, double>> vpdouble;

typedef vector<vector<int>> vvint;
typedef vector<vector<ll>> vvll;
typedef vector<vpint> vvpint;
typedef vector<vpll> vvpll;
typedef vector<vector<double>> vvdouble;
typedef vector<vector<string>> vvstring;
typedef vector<vector<bool>> vvbool;



typedef vector<vector<vector<ll>>> vvvll;
typedef vector<vector<vector<bool>>> vvvbool;

const int INF = 1e9 + 1;
const ll LLINF = 1e17 + 1;
const int DX[9] = { 0,  0, 1, -1, 1,  1, -1, -1, 0 }; // 4;４近傍
const int DY[9] = { 1, -1, 0,  0, 1, -1,  1, -1, 0 }; // 8:８近傍 9:(0,0)を含む
const double PI = 3.14159265358979323846264338327950288;

//VVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVV

const ll MOD = 1000000007; //10^9 + 7

//VVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVV


template<class T>bool chmax(T& a, const T& b) { if (a < b) { a = b; return 1; } else return false; }
template<class T>bool chmin(T& a, const T& b) { if (b < a) { a = b; return 1; } else return false; }


//---------------------------------------------------------------
//  オーバーフローチェック
//---------------------------------------------------------------
void is_overflow(ll a, ll b) { if ((a * b) / b != a) cout << "OVERFLOW!!!!!" << endl; }

//---------------------------------------------------------------
//  整数の乱数生成
//---------------------------------------------------------------
ll random_int(ll start, ll last)
{
    //srand((uint)time(NULL));
    return start + rand() % (last - start + 1);
}

//---------------------------------------------------------------
//  x∈[a, b)
//---------------------------------------------------------------
bool is_in(ll x, ll a, ll b)
{
    return (a <= x && x < b);
}

//---------------------------------------------------------------
//  約数列挙
//---------------------------------------------------------------
vll divisor(ll n) {
    vll ret;
    for (ll i = 1; i * i <= n; i++) { if (n % i == 0) { ret.push_back(i);	if (i * i != n) ret.push_back(n / i); } }
    sort(begin(ret), end(ret));	return (ret);
}

//---------------------------------------------------------------
// N以下のすべての素数を列挙する(エラトステネスの篩)
//---------------------------------------------------------------
vbool searchSosuu(ll N) {
    vbool sosuu;
    for (ll i = 0; i < N; i++) { sosuu.emplace_back(true); }
    sosuu[0] = false;	sosuu[1] = false;
    for (ll i = 2; i < N; i++) { if (sosuu[i]) { for (ll j = 2; i * j < N; j++) { sosuu[i * j] = false; } } }
    return sosuu;
}

//---------------------------------------------------------------
// 素因数分解　O(√N)
//---------------------------------------------------------------
vpll to_prime(ll n) {
    vpll prime_factor;
    for (ll i = 2; i * i <= n; i++) {
        ll count = 0; while (n % i == 0) { count++; n /= i; }
        if (count) { pair<ll, ll> temp = { i, count };	prime_factor.emplace_back(temp); }
    }
    if (n != 1) { pair<ll, ll> temp = { n, 1 }; prime_factor.emplace_back(temp); }
    return prime_factor;
}

//---------------------------------------------------------------
// 高速素因数分解(前処理O(N), 分解O(logN))
//---------------------------------------------------------------
class FastPrime
{
public:
    vll div;
    vbool is_sosuu;

    FastPrime(ll N) : div(N + 10, -1), is_sosuu(N + 10, true)
    {
        for (ll i = 2; i < N; i++)
            if (div[i] == -1)
                for (ll j = 2; i * j <= N; j++)
                {
                    div[i * j] = i;
                    is_sosuu[i * j] = false;
                }
    }

    vpll to_prime(ll N)
    {
        if (N == 1) return vpll({});

        vll divs;
        while (div[N] != -1)
        {
            divs.emplace_back(div[N]);
            N /= div[N];
        }
        if (N > 1) divs.emplace_back(N);

        sort(divs.begin(), divs.end());

        vpll primes;
        ll count = 1;
        for (int i = 1; i < divs.size(); i++)
        {
            if (divs[i] > divs[i - 1])
            {
                primes.emplace_back(pll(divs[i - 1], count));
                count = 0;
            }
            count++;
        }
        primes.emplace_back(pll(divs[divs.size() - 1], count));

        return primes;
    }

};

//---------------------------------------------------------------
// 最大公約数（ユークリッドの互除法）
//---------------------------------------------------------------
ll gcd(ll a, ll b) {
    if (a < b) { ll tmp = a;	a = b; b = tmp; }
    ll r = a % b;
    while (r != 0) { a = b; b = r; r = a % b; }
    return b;
}

//---------------------------------------------------------------
// 最小公倍数
//---------------------------------------------------------------
ll lcm(ll a, ll b) { ll temp = gcd(a, b); return temp * (a / temp) * (b / temp); }

//---------------------------------------------------------------
// 階乗
//---------------------------------------------------------------
ll factorial(ll n) { if (n <= 1) { return 1; }return (n * (factorial(n - 1))) % MOD; }

//---------------------------------------------------------------
// 高速コンビネーション計算(前処理:O(N) 計算:O(1))
//---------------------------------------------------------------
// テーブルを作る前処理
ll comb_const = 300005;
vll fac(comb_const), finv(comb_const), inv(comb_const);
bool COMineted = false;
void COMinit(ll mod = MOD) {
    fac[0] = fac[1] = 1; finv[0] = finv[1] = 1; inv[1] = 1;
    for (ll i = 2; i < comb_const; i++) {
        fac[i] = fac[i - 1] * i % mod;
        inv[i] = mod - inv[mod % i] * (mod / i) % mod;
        finv[i] = finv[i - 1] * inv[i] % mod;
    }
    COMineted = true;
}
// 二項係数計算
ll COM(ll n, ll k, ll mod = MOD) {
    if (COMineted == false) COMinit(mod);
    if (n < k) return 0;
    if (n < 0 || k < 0) return 0;
    return (fac[n] * (finv[k] * finv[n - k] % mod)) % mod;
}

//---------------------------------------------------------------
// 繰り返し２乗法 base^sisuu
//---------------------------------------------------------------
ll RepeatSquaring(ll base, ll sisuu, ll mod = MOD) {
    if (sisuu < 0) { cout << "RepeatSquaring: 指数が負です!" << endl; return 0; }
    if (sisuu == 0) return 1;
    if (sisuu % 2 == 0) { ll t = RepeatSquaring(base, sisuu / 2, mod) % mod;	return (t * t) % mod; }
    return (base * RepeatSquaring(base, sisuu - 1, mod)) % mod;
}

//---------------------------------------------------------------
// 高速単発コンビネーション計算(O(logN))
//---------------------------------------------------------------
ll fast_com(ll a, ll b, ll mod = MOD) {
    ll bunshi = 1;	ll bunbo = 1;
    for (ll i = 1; i <= b; i++) { bunbo *= i;	bunbo %= mod; bunshi *= (a - i + 1); bunshi %= mod; }
    ll ret = bunshi * RepeatSquaring(bunbo, mod - 2, mod); ret %= mod;
    while (ret < 0) { ret += mod; }
    return ret;
}

//---------------------------------------------------------------
// 整数をビットのリストに変換する ll->vbool
//---------------------------------------------------------------
vbool to_bitlist(ll bit, ll fixed_size = 1) {
    if (bit == 0) return vbool(fixed_size, 0);
    vbool list;
    while (bit > 0) { list.emplace_back(bit & 1);	bit /= 2; }
    while (list.size() < fixed_size) { list.emplace_back(0); }
    return list;
}

//---------------------------------------------------------------
// 座標圧縮(O(NlogN))   0スタートになることに注意！
//---------------------------------------------------------------
class PosPress
{
    /*
    配列Pを座圧→instance = PosPress(P);

    座圧済み配列→instance.pressed
    fooの圧縮後→instance.func[foo]
    fooの圧縮前→instance.rev[foo]
    */
public:
    vll pressed;
    map<ll, ll> func;
    map<ll, ll> rev;

    PosPress(vll P) {
        pressed = P; sort(P.begin(), P.end()); func[P[0]] = 0;	rev[0] = P[0]; ll next = 1;
        for (int i = 1; i < P.size(); i++) { if (P[i] != P[i - 1]) { func[P[i]] = next; rev[next] = P[i]; next++; } }
        for (int i = 0; i < P.size(); i++) { pressed[i] = func[pressed[i]]; }
    }
};

//---------------------------------------------------------------
// 行列累乗(O(N^3))
//---------------------------------------------------------------
vvll mat_cross(vvll A, vvll B) {
    ll N = A.size(); ll K = B.size(); ll M = B[0].size();
    vvll C(N, vll(M));
    for (int i = 0; i < N; i++)
        for (int j = 0; j < M; j++)
            for (int k = 0; k < K; k++)
                C[i][j] += A[i][k] * B[k][j];
    return C;
}

//---------------------------------------------------------------
// 2直線の交差判定(直線(x1, y1)->(x2, y2) と 直線(X1, Y1)->(X2, Y2))
//---------------------------------------------------------------
bool is_cross(ll x1, ll y1, ll x2, ll y2, ll X1, ll Y1, ll X2, ll Y2) {
    ll dx_ai = X1 - x1;	ll dy_ai = Y1 - y1;
    ll dx_bi = X1 - x2;	ll dy_bi = Y1 - y2;
    ll dx_ai2 = X2 - x1; ll dy_ai2 = Y2 - y1;
    ll dx_bi2 = X2 - x2; ll dy_bi2 = Y2 - y2;
    ll si = dx_ai * dy_bi - dy_ai * dx_bi;
    ll si2 = dx_ai2 * dy_bi2 - dy_ai2 * dx_bi2;
    ll si3 = dx_ai * dy_ai2 - dy_ai * dx_ai2;
    ll si4 = dx_bi * dy_bi2 - dy_bi * dx_bi2;
    return (si * si2 < 0 && si3 * si4 < 0);
}

//---------------------------------------------------------------
// 最長増加部分列の長さ(O(NlogN))
//---------------------------------------------------------------
ll LSI(vll vec)
{
    ll size = vec.size();
    vll lsi(size + 1); // 長さjを作った時の右端の最小値
    for (ll i = 0; i <= size; i++) { lsi[i] = LLINF; }
    lsi[0] = 0;	lsi[1] = vec[0];
    for (ll i = 1; i < size; i++)
    {
        // 初めてvec[i]の方が小さくなるところを探す
        auto Iter = lower_bound(lsi.begin(), lsi.end(), vec[i]);
        ll idx = Iter - lsi.begin();
        if (idx > 0 && lsi[idx - 1] < vec[i]) { lsi[idx] = vec[i]; }
    }
    for (ll i = size; i >= 0; i--) { if (lsi[i] < LLINF) { return i; } }
}

//---------------------------------------------------------------
// LCS(最長共通部分列) O(|S||T|)
//---------------------------------------------------------------
string LCS(string S, string T)
{
    vvll dp(S.length() + 1);
    for (int i = 0; i < dp.size(); i++) { vll t(T.length() + 1, 0); dp[i] = t; }

    for (int i = 0; i < S.length(); i++) {
        for (int j = 0; j < T.length(); j++) {
            dp[i + 1][j + 1] = max({ dp[i][j] + ll(S[i] == T[j]), dp[i + 1][j], dp[i][j + 1], dp[i + 1][j + 1] });
        }
    }
    ll len = dp[S.length()][T.length()];
    string ans = "";
    ll i = dp.size() - 1;
    ll j = dp[0].size() - 1;
    while (len > 0) {
        if (dp[i - 1][j] == len) { i--; }
        else if (dp[i][j - 1] == len) { j--; }
        else { ans += S[i - 1]; i--; j--; len--; }
    }

    reverse(ans.begin(), ans.end());
    return ans;
}
vll LCS(vll S, vll T)
{
    vvll dp(S.size() + 1);
    for (int i = 0; i < dp.size(); i++) { vll t(T.size() + 1, 0); dp[i] = t; }

    for (int i = 0; i < S.size(); i++) {
        for (int j = 0; j < T.size(); j++) {
            dp[i + 1][j + 1] = max({ dp[i][j] + ll(S[i] == T[j]), dp[i + 1][j], dp[i][j + 1], dp[i + 1][j + 1] });
        }
    }
    ll len = dp[S.size()][T.size()];
    vll ans;
    ll i = dp.size() - 1;
    ll j = dp[0].size() - 1;
    while (len > 0) {
        if (dp[i - 1][j] == len) { i--; }
        else if (dp[i][j - 1] == len) { j--; }
        else { ans.emplace_back(S[i - 1]); i--; j--; len--; }
    }

    reverse(ans.begin(), ans.end());
    return ans;
}

//---------------------------------------------------------------
// 木の根からの深さ
//---------------------------------------------------------------
vll tree_depth(vvll edge, ll start_node)
{
    ll n_node = edge.size();
    vll dist(n_node, LLINF);
    dist[start_node] = 0;

    stack<pll> S;
    S.push({ start_node, 0 });

    while (!S.empty())
    {
        ll node = S.top().first;
        ll d = S.top().second;
        dist[node] = d;

        S.pop();

        for (int i = 0; i < edge[node].size(); i++)
        {
            if (dist[edge[node][i]] == LLINF)
            {
                S.push({ edge[node][i], d + 1 });
            }
        }
    }

    return dist;
}

//---------------------------------------------------------------
// ワーシャルフロイド法(O(N^3)) d: 正方行列(N*N)
//---------------------------------------------------------------
vvll warshall_floyd(vvll d) {
    ll n = d.size();
    for (int k = 0; k < n; k++) {       // 経由する頂点
        for (int i = 0; i < n; i++) {    // 始点
            for (int j = 0; j < n; j++) {  // 終点
                d[i][j] = min(d[i][j], d[i][k] + d[k][j]);
            }
        }
    }
    return d;
}

//---------------------------------------------------------------
// Union Find
//---------------------------------------------------------------
class UnionFind {
public:
    /*
    UnionFind uf(要素の個数);
    for(int i = 0;i < 関係の個数; i++)
    {
        uf.merge(A[i], B[i]);
    }

    nを含む集合の大きさ = uf.size(n)
    nを含む集合の代表者 = uf.root(n)
    集合の個数 = uf.n_group
    */
    vector <ll> par; // 各元の親を表す配列
    vector <ll> siz; // 素集合のサイズを表す配列(1 で初期化)
    ll n_group; //集合の数

    // Constructor
    UnionFind(ll sz_) : par(sz_), siz(sz_, 1LL) {
        for (ll i = 0; i < sz_; ++i) par[i] = i; // 初期では親は自分自身
        n_group = sz_;
    }
    void init(ll sz_) {
        par.resize(sz_);
        siz.assign(sz_, 1LL);  // resize だとなぜか初期化されなかった
        for (ll i = 0; i < sz_; ++i) par[i] = i; // 初期では親は自分自身
    }

    // Member Function
    // Find
    ll root(ll x) { // 根の検索
        while (par[x] != x) {
            x = par[x] = par[par[x]]; // x の親の親を x の親とする
        }
        return x;
    }

    // Union(Unite, Merge)
    bool merge(ll x, ll y) {
        x = root(x);
        y = root(y);
        if (x == y) return false;
        // merge technique（データ構造をマージするテク．小を大にくっつける）
        if (siz[x] < siz[y]) swap(x, y);
        siz[x] += siz[y];
        par[y] = x;
        n_group--;
        return true;
    }

    bool issame(ll x, ll y) { // 連結判定
        return root(x) == root(y);
    }

    ll size(ll x) { // 素集合のサイズ
        return siz[root(x)];
    }
};

//---------------------------------------------------------------
// ダイクストラ(O(ElogV))   edge: 隣接リスト from->pair{to, cost}
//---------------------------------------------------------------
class Dijkstra
{
public:

    vll dist; // iまでの最短距離
    vll past; // (iまで最短で行くときの一つ前)

    // edge[i] -> {to, cost}
    Dijkstra(vvpll edge, ll start) : dist(edge.size(), LLINF), past(edge.size(), -1)
    {
        using Pi = pll;
        priority_queue< Pi, vector< Pi >, greater< Pi > > que;
        dist[start] = 0;
        que.emplace(dist[start], start);
        while (!que.empty()) {
            ll cost;
            int idx;
            tie(cost, idx) = que.top();
            que.pop();
            if (dist[idx] < cost) continue;
            for (int i = 0; i < edge[idx].size(); i++)
            {
                ll next_cost = cost + edge[idx][i].second;
                if (dist[edge[idx][i].first] <= next_cost) continue;
                dist[edge[idx][i].first] = next_cost;
                past[edge[idx][i].first] = idx;
                que.emplace(dist[edge[idx][i].first], edge[idx][i].first);
            }
        }
    }

    // goalまでの最短経路
    vll shortest(ll goal)
    {
        vll ret;
        while (goal != -1)
        {
            ret.emplace_back(goal);
            goal = past[goal];
        }
        reverse(ret.begin(), ret.end());
        return ret;
    }
};

//---------------------------------------------------------------
// LCA: 最近共通祖先 (O())
//---------------------------------------------------------------
class Lca
{
public:

    vll depth; // 根0からiまでの最短距離
    vvll doubling;
    ll n_bit = 30;

    // edge[i] -> {to, cost}
    Lca(vvll edge, ll root = 0) : doubling(50, vll(edge.size(), -1))
    {
        // 深さ
        depth = tree_depth(edge, root);

        // ダブリングで親を辿れるようにする
        // jから2^i回親を辿ったノード
        doubling[0][0] = -1;
        for (int i = 1; i < edge.size(); i++)
            for (int j : edge[i])
                if (depth[i] > depth[j]) { doubling[0][i] = j; break; }
        for (int i = 1; i < n_bit; i++)
            for (int j = 0; j < edge.size(); j++) {
                if (doubling[i - 1][j] != -1) doubling[i][j] = doubling[i - 1][doubling[i - 1][j]];
                else doubling[i][j] = -1;
            }
    }

    // aとbの最近共通祖先
    ll get_lca(ll a, ll b)
    {
        // depth[a] >= depth[b]にする
        if (depth[a] < depth[b]) swap(a, b);
        ll oa = a;
        ll ob = b;
        ll d = depth[a] - depth[b];

        // aをdだけさかのぼる。
        vbool bit = to_bitlist(d, n_bit);
        for (int i = 0; i < n_bit; i++)if (bit[i]) a = doubling[i][a];

        // depth[a] == depth[b]になっている。
        for (int i = n_bit - 1; i >= 0; i--) {
            if (doubling[i][a] == doubling[i][b]) continue;
            a = doubling[i][a];	b = doubling[i][b];
        }
        return a == b ? a : doubling[0][a];
    }


};

//---------------------------------------------------------------
// Z-algorithm(SとS[i:]の最長接頭辞長)  O(|S|)
//---------------------------------------------------------------
vll Zalgorithm(string S)
{
    ll n = S.size();
    vll Z(n, 0);
    ll start = -1;
    ll last = -1;
    for (ll i = 1; i < n; i++) {
        if (start >= 0) { Z[i] = min(Z[i - start], last - i); chmax(Z[i], 0LL); }
        while (i + Z[i] < S.size() && S[Z[i]] == S[i + Z[i]])
            Z[i] ++;
        if (last < i + Z[i]) { last = i + Z[i]; start = i; }
    }
    Z[0] = n;
    return Z;
}
vll Zalgorithm(vll S)
{
    ll n = S.size();
    vll Z(n, 0);
    ll start = -1;
    ll last = -1;
    for (ll i = 1; i < n; i++) {
        if (start >= 0) { Z[i] = min(Z[i - start], last - i); chmax(Z[i], 0LL); }
        while (i + Z[i] < S.size() && S[Z[i]] == S[i + Z[i]])
            Z[i] ++;
        if (last < i + Z[i]) { last = i + Z[i]; start = i; }
    }
    Z[0] = n;
    return Z;
}

//---------------------------------------------------------------
// 二部グラフ判定(O(E))  edge -> リスト
//---------------------------------------------------------------
bool is_bipartite(vvll edge)
{
    ll N = edge.size();
    vll color(N, -1);
    color[0] = 0;
    queue<ll> Q;
    Q.push(0);
    while (!Q.empty())
    {
        ll now = Q.front();
        Q.pop();

        for (int i : edge[now])
        {
            if (color[i] == -1)
            {
                color[i] = (color[now] == 0 ? 1 : 0);
                Q.push(i);
            }
            else if (color[i] == color[now])
            {
                return false;
            }
        }
    }
    return true;
}

//---------------------------------------------------------------
// セグメント木
//---------------------------------------------------------------
class SegmentTree
{
public:

    const ll SEG_LEN = 1 << 19;
    vector<ll> seg;
    ll s;
    ll E;

    SegmentTree(ll N, ll e) : seg(SEG_LEN * 2, e) {
        s = N;
        E = e;
    }

    ll func(ll a, ll b)
    {
        return a + b;
    }

    void set(ll p, ll to)
    {
        ll pos = p + SEG_LEN;
        seg[pos] = to;
        while (true)
        {
            pos /= 2;
            if (pos <= 0) break;

            seg[pos] = func(seg[pos * 2], seg[pos * 2 + 1]);
        }
    }

    void add(ll p, ll d)
    {
        ll pos = p + SEG_LEN;
        seg[pos] += d;
        while (true)
        {
            pos /= 2;
            if (pos <= 0) break;

            seg[pos] = func(seg[pos * 2], seg[pos * 2 + 1]);
        }
    }

    ll get(ll left, ll right)
    {
        left += SEG_LEN;
        right += SEG_LEN + 1;

        ll ret = E;

        while (left < right)
        {
            while (left % 2 == 1)
            {
                ret = func(ret, seg[left]);
                left++;
            }
            while (right % 2 == 1)
            {
                ret = func(ret, seg[right - 1]);
                right--;
            }

            left /= 2;
            right /= 2;
        }

        return ret;
    }

};

//---------------------------------------------------------------
// ダブリング
//---------------------------------------------------------------
class Doubling
{
public:

    ll M = 100;
    vvll doubling;

    Doubling(vll to) : doubling(M, vll(to.size(), -1))
    {
        ll N = to.size();
        for (int i = 0; i < N; i++) doubling[0][i] = to[i];
        for (int i = 1; i < M; i++)
            for (int j = 0; j < N; j++)
                doubling[i][j] = doubling[i - 1][doubling[i - 1][j]];
    }

    ll destination(ll from, ll K)
    {
        vbool bits = to_bitlist(K);
        ll now = from;
        for (int i = 0; i < bits.size(); i++)
        {
            if (bits[i])
            {
                now = doubling[i][now];
            }
        }
        return now;
    }

};

//========================================================================
//========================================================================
//========================================================================
//========================================================================

long double EPS = 1e-10;
long double add(long double a, long double b)
{
    if (abs(a + b) < EPS * (abs(a) + abs(b))) return 0;
    return a + b;
}

struct P
{
    long double x, y;
    P() {}
    P(long double x, long double y): x(x), y(y) {
    }

    P operator + (P p)
    {
        return P(add(x, p.x), add(y, p.y));
    }
    P operator -(P p)
    {
        return P(add(x, -p.x), add(y, -p.y));
    }

    P operator *(long double d)
    {
        return P(x * d, y * d);
    }
    long double dot(P p)
    {
        return add(x * p.x, y * p.y);
    }

    long double det(P p)
    {
        return add(x * p.y, -y * p.x);
    }


};

bool cmp_x(const P& p, const P& q)
{
    if (p.x != q.x) return p.x < q.x;
    return p.y < q.y;
}

vector<P> convex_hull(P* ps, int n)
{
    sort(ps, ps + n, cmp_x);
    int k = 0;
    vector<P> qs(n + 2);

    for (int i = 0; i < n; i++)
    {
        while (k > 1 && (qs[k - 1] - qs[k - 2]).det(ps[i] - qs[k - 1]) <= 0)k--;
        qs[k++] = ps[i];
    }

    for (int i = n - 2, t = k; i >= 0; i--) {

        while (k > 1 && (qs[k - 1] - qs[k - 2]).det(ps[i] - qs[k - 1]) <= 0)k--;
        qs[k++] = ps[i];
    }

    qs.resize(k - 1);
    return qs;

}

ll dist(P p, P q)
{
    return abs(p.x - q.x) + abs(p.y - q.y);
}



P ps[ll(2 * 1e5 + 10)];
int main() {

    //////==================================
    cin.tie(nullptr);
    ios_base::sync_with_stdio(false);
    cout << fixed << setprecision(25);
    //////==================================


    /*
    ～思いついたことはとりあえず絶対メモする！！～
    */

    ll N;
    cin >> N;

    for (int i = 0; i < N; i++)
    {
        ll x, y;
        cin >> x >> y;
        ps[i] = P(x, y);
    }

    vector<P> qs = convex_hull(ps, N);



    if (N * N < 1e8)
    {
        ll ans = 0;
        for (int i = 0; i < N; i++)
        {
            for (int j = i + 1; j < N; j++)
            {
                chmax(ans, dist(ps[i], ps[j]));
            }
        }
        cout << ans << endl;
        return 0;
    }






    int n = qs.size();
    if (n == 2)
    {
        cout << dist(qs[0], qs[1]);
        return 0;
    }

    int i = 0, j = 0;
    for (int k = 0; k < n; k++)
    {
        if (!cmp_x(qs[i], qs[k])) i = k;
        if (cmp_x(qs[j], qs[k])) j = k;
    }

    ll ans = 0;
    int si = i;
    int sj = j;
    while (i != sj || j != si)
    {
        chmax(ans, dist(qs[i], qs[j]));
        if ((qs[(i + 1) % n] - qs[i]).det(qs[(j + 1) % n] - qs[j]) < 0) {
            i = (i + 1) % n;
        }
        else
        {
            j = (j + 1) % n;
        }
    }

    cout << ans;




}


Measured memory_bytes: 16728