Problem: You are given positions (X_i, Y_i) of N enemy rooks on an infinite chessboard. No two rooks attack each other (at most one rook per row or column).

You're going to replace one rook with a king and then move the king repeatedly to beat as many rooks as possible.

You can't enter a cell that is being attacked by a rook. Additionally, you can't move diagonally to an empty cell (but you can beat a rook diagonally).

(So this king moves like a superpawn that beats diagonally in 4 directions and moves horizontally/vertically in 4 directions.)

For each rook, consider replacing it with a king, and find the minimum possible number of moves needed to beat the maximum possible number of rooks.

Constraints

* 2 \leq N \leq 200\,000
* 1 \leq X_i, Y_i \leq 10^6
* X_i \neq X_j
* Y_i \neq Y_j
* All values in input are integers.

Input

Input is given from Standard Input in the following format.


N
X_1 Y_1
X_2 Y_2
\vdots
X_N Y_N


Output

Print N lines. The i-th line is for scenario of replacing the rook at (X_i, Y_i) with your king. This line should contain one integer: the minimum number of moves to beat M_i rooks where M_i denotes the maximum possible number of beaten rooks in this scenario (in infinite time).

Examples

Input

6
1 8
6 10
2 7
4 4
9 3
5 1


Output

5
0
7
5
0
0


Input

5
5 5
100 100
70 20
81 70
800 1


Output

985
985
1065
1034
0


Input

10
2 5
4 4
13 12
12 13
14 17
17 19
22 22
16 18
19 27
25 26


Output

2
2
9
9
3
3
24
5
0
25

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;
 
typedef long long ll;
typedef long double ld;
typedef double db; 
typedef string str; 

typedef pair<int,int> pi;
typedef pair<ll,ll> pl; 
typedef pair<db,db> pd; 

typedef vector<int> vi; 
typedef vector<ll> vl; 
typedef vector<db> vd; 
typedef vector<str> vs; 
typedef vector<pi> vpi;
typedef vector<pl> vpl; 
typedef vector<pd> vpd; 

#define mp make_pair
#define f first
#define s second
#define sz(x) (int)(x).size()
#define all(x) begin(x), end(x)
#define rall(x) (x).rbegin(), (x).rend() 
#define rsz resize
#define ins insert 
#define ft front() 
#define bk back()
#define pf push_front 
#define pb push_back
#define eb emplace_back 
#define lb lower_bound 
#define ub upper_bound 

#define FOR(i,a,b) for (int i = (a); i < (b); ++i)
#define F0R(i,a) FOR(i,0,a)
#define ROF(i,a,b) for (int i = (b)-1; i >= (a); --i)
#define R0F(i,a) ROF(i,0,a)
#define trav(a,x) for (auto& a: x)

const int MOD = 1e9+7; // 998244353;
const int MX = 2e5+5; 
const ll INF = 1e18; 
const ld PI = acos((ld)-1);
const int xd[4] = {1,0,-1,0}, yd[4] = {0,1,0,-1}; 
mt19937 rng((uint32_t)chrono::steady_clock::now().time_since_epoch().count()); 

template<class T> bool ckmin(T& a, const T& b) { 
    return b < a ? a = b, 1 : 0; }
template<class T> bool ckmax(T& a, const T& b) { 
    return a < b ? a = b, 1 : 0; } 
constexpr int pct(int x) { return __builtin_popcount(x); } 
constexpr int bits(int x) { return 31-__builtin_clz(x); } // floor(log2(x)) 
ll cdiv(ll a, ll b) { return a/b+((a^b)>0&&a%b); } // divide a by b rounded up
ll fdiv(ll a, ll b) { return a/b-((a^b)<0&&a%b); } // divide a by b rounded down
ll half(ll x) { return fdiv(x,2); }

template<class T, class U> T fstTrue(T lo, T hi, U f) {
    hi ++; assert(lo <= hi); // assuming f is increasing
    while (lo < hi) { // find first index such that f is true 
        T mid = half(lo+hi);
        f(mid) ? hi = mid : lo = mid+1; 
    } 
    return lo;
}
template<class T, class U> T lstTrue(T lo, T hi, U f) {
    lo --; assert(lo <= hi); // assuming f is decreasing
    while (lo < hi) { // find first index such that f is true 
        T mid = half(lo+hi+1);
        f(mid) ? lo = mid : hi = mid-1;
    } 
    return lo;
}
template<class T> void remDup(vector<T>& v) { 
    sort(all(v)); v.erase(unique(all(v)),end(v)); }

// INPUT
template<class A> void re(complex<A>& c);
template<class A, class B> void re(pair<A,B>& p);
template<class A> void re(vector<A>& v);
template<class A, size_t SZ> void re(array<A,SZ>& a);

template<class T> void re(T& x) { cin >> x; }
void re(db& d) { str t; re(t); d = stod(t); }
void re(ld& d) { str t; re(t); d = stold(t); }
template<class H, class... T> void re(H& h, T&... t) { re(h); re(t...); }

template<class A> void re(complex<A>& c) { A a,b; re(a,b); c = {a,b}; }
template<class A, class B> void re(pair<A,B>& p) { re(p.f,p.s); }
template<class A> void re(vector<A>& x) { trav(a,x) re(a); }
template<class A, size_t SZ> void re(array<A,SZ>& x) { trav(a,x) re(a); }

// TO_STRING
#define ts to_string
str ts(char c) { return str(1,c); }
str ts(const char* s) { return (str)s; }
str ts(str s) { return s; }
str ts(bool b) { 
    #ifdef LOCAL
        return b ? "true" : "false"; 
    #else 
        return ts((int)b);
    #endif
}
template<class A> str ts(complex<A> c) { 
    stringstream ss; ss << c; return ss.str(); }
str ts(vector<bool> v) {
    str res = "{"; F0R(i,sz(v)) res += char('0'+v[i]);
    res += "}"; return res; }
template<size_t SZ> str ts(bitset<SZ> b) {
    str res = ""; F0R(i,SZ) res += char('0'+b[i]);
    return res; }
template<class A, class B> str ts(pair<A,B> p);
template<class T> str ts(T v) { // containers with begin(), end()
    #ifdef LOCAL
        bool fst = 1; str res = "{";
        for (const auto& x: v) {
            if (!fst) res += ", ";
            fst = 0; res += ts(x);
        }
        res += "}"; return res;
    #else
        bool fst = 1; str res = "";
        for (const auto& x: v) {
            if (!fst) res += " ";
            fst = 0; res += ts(x);
        }
        return res;

    #endif
}
template<class A, class B> str ts(pair<A,B> p) {
    #ifdef LOCAL
        return "("+ts(p.f)+", "+ts(p.s)+")"; 
    #else
        return ts(p.f)+" "+ts(p.s);
    #endif
}

// OUTPUT
template<class A> void pr(A x) { cout << ts(x); }
template<class H, class... T> void pr(const H& h, const T&... t) { 
    pr(h); pr(t...); }
void ps() { pr("\n"); } // print w/ spaces
template<class H, class... T> void ps(const H& h, const T&... t) { 
    pr(h); if (sizeof...(t)) pr(" "); ps(t...); }

// DEBUG
void DBG() { cerr << "]" << endl; }
template<class H, class... T> void DBG(H h, T... t) {
    cerr << ts(h); if (sizeof...(t)) cerr << ", ";
    DBG(t...); }
#ifdef LOCAL // compile with -DLOCAL, chk -> fake assert
    #define dbg(...) cerr << "Line(" << __LINE__ << ") -> [" << #__VA_ARGS__ << "]: [", DBG(__VA_ARGS__)
    #define chk(...) if (!(__VA_ARGS__)) cerr << "Line(" << __LINE__ << ") -> function(" \
         << __FUNCTION__  << ") -> CHK FAILED: (" << #__VA_ARGS__ << ")" << "\n", exit(0);
#else
    #define dbg(...) 0
    #define chk(...) 0
#endif

// FILE I/O
void setIn(str s) { freopen(s.c_str(),"r",stdin); }
void setOut(str s) { freopen(s.c_str(),"w",stdout); }
void unsyncIO() { ios_base::sync_with_stdio(0); cin.tie(0); }
void setIO(str s = "") {
    unsyncIO();
    // cin.exceptions(cin.failbit); 
    // throws exception when do smth illegal
    // ex. try to read letter into int
    if (sz(s)) { setIn(s+".in"), setOut(s+".out"); } // for USACO
}

const int mx = 200005;

int N;
pl P[mx];
map<int, int> m;  //compress y 
map<int, int> toind; // original index of x coor
ll ans[mx];

ll getDist(int i, int j){
    return abs(P[j].f-P[i].f)+abs(P[j].s-P[i].s);
}

pl search(int l, int r, int L, int R){
    dbg(l, r, L, R);
    int dir = 0;
    if(l-1 >= 1){
        if(m[P[l-1].s] == L-1) dir = 1;
        else if(m[P[l-1].s] == R+1) dir = 2;
    }
    if(r+1 <= N){
        if(m[P[r+1].s] == R+1) dir = 1;
        else if(m[P[r+1].s] == L-1) dir = 2;
    }
    dbg(dir);
    if(dir == 0) return mp(-(r-l), -(r-l));

    int lind = l;
    int rind = r;

    for(int i = l-1; i >= 1; i--){
        if(dir == 1 && m[P[i].s] == i-l+L){
            lind = i;
        }
        else if(dir == 2 && m[P[i].s] == R-i+l){
            lind = i;
        }
        else break;
    }

    for(int i = r+1; i <= N; i++){
        if(dir == 1 && m[P[i].s] == i-r+R){
            rind = i;
        }
        else if(dir == 2 && m[P[i].s] == L-i+r){
            rind = i;
        }
        else break;
    }

    int nL, nR;
    if(dir == 1){
        nL = min(L, m[P[lind].s]);
        nR = max(R, m[P[rind].s]);
    }
    else{
        nL = min(L, m[P[rind].s]);
        nR = max(R, m[P[lind].s]);
    }

    pl val = search(lind, rind, nL, nR);
    pl res = mp(INF, INF);
    if(lind == l){
        ckmin(res.f, val.s+getDist(l, rind));
        ckmin(res.s, val.s+getDist(r, rind));
    }
    if(rind == r){
        ckmin(res.f, val.f+getDist(l, lind));
        ckmin(res.s, val.f+getDist(r, lind));
    }
    ckmin(res.f, val.f+getDist(l, rind)+getDist(rind, lind));
    ckmin(res.f, val.s+getDist(l, lind)+getDist(lind, rind));
    ckmin(res.s, val.f+getDist(r, rind)+getDist(rind, lind));
    ckmin(res.s, val.s+getDist(r, lind)+getDist(lind, rind));
    
    dbg(res);
    return res;
}

int main() {
    setIO();
    cin >> N;
    vpi v;
    for(int i = 1; i <= N; i++){
        cin >> P[i].f >> P[i].s;
        m[P[i].s];
        toind[P[i].f] = i;
    }
    int cnt = 0;
    for(auto &u: m){
        u.s = ++cnt;
    }
    sort(P+1, P+1+N);
    for(int i = 1; i <= N; i++){
        if(i-1 >= 1 && m[P[i-1].s] == m[P[i].s]-1) continue;
        if(i-1 >= 1 && m[P[i-1].s] == m[P[i].s]+1) continue;
        if(i+1 > N){
            ans[toind[P[i].f]] = 0;
            continue;
        }
        //edit i after finding a range
        if(m[P[i+1].s] == m[P[i].s]+1){
            int maxi = i+1;
            for(int j = i+1; j <= N; j++){
                if(m[P[j].s] == m[P[i].s]+j-i){
                    maxi = j;
                }
                else break;
            }
            pl x = search(i, maxi, m[P[i].s], m[P[i].s]+maxi-i);
            for(int j = i; j <= maxi; j++){
                ans[toind[P[j].f]] = min(x.f+getDist(j, maxi)+getDist(i, maxi), x.s+getDist(j, i)+getDist(i, maxi));
            }
            dbg(i, maxi);
            i = maxi;
        }
        else if(m[P[i+1].s] == m[P[i].s]-1){
            int maxi = i+1;
            for(int j = i+1; j <= N; j++){
                if(m[P[j].s] == m[P[i].s]-j+i){
                    maxi = j;
                }
                else break;
            }
            pl x = search(i, maxi, m[P[i].s]-maxi+i, m[P[i].s]);
            for(int j = i; j <= maxi; j++){
                ans[toind[P[j].f]] = min(x.f+getDist(j, maxi)+getDist(i, maxi), x.s+getDist(j, i)+getDist(i, maxi));
            }
            dbg(i, maxi);
            i = maxi;
        }
        else{
            ans[toind[P[i].f]] = 0;
        }
        
    }

    for(int i = 1; i <= N; i++){
        ps(ans[i]);
    }

    // you should actually read the stuff at the bottom
}

/* stuff you should look for
    * int overflow, array bounds
    * special cases (n=1?)
    * do smth instead of nothing and stay organized
    * WRITE STUFF DOWN
*/