Problem:
Score : 600 points

Problem Statement

For a non-negative integer K, we define a fractal of level K as follows:

A fractal of level 0 is a grid with just one white square.

When K > 0, a fractal of level K is a 3^K \times 3^K grid. If we divide this grid into nine 3^{K-1} \times 3^{K-1} subgrids:

The central subgrid consists of only black squares.

Each of the other eight subgrids is a fractal of level K-1.

For example, a fractal of level 2 is as follows:

In a fractal of level 30, let (r, c) denote the square at the r-th row from the top and the c-th column from the left.

You are given Q quadruples of integers (a_i, b_i, c_i, d_i).
For each quadruple, find the distance from (a_i, b_i) to (c_i, d_i).

Here the distance from (a, b) to (c, d) is the minimum integer n that satisfies the following condition:

There exists a sequence of white squares (x_0, y_0), \ldots, (x_n, y_n) satisfying the following conditions:

(x_0, y_0) = (a, b)

(x_n, y_n) = (c, d)

For every i (0 \leq i \leq n-1), (x_i, y_i) and (x_{i+1}, y_{i+1}) share a side.

Constraints

1 \leq Q \leq 10000

1 \leq a_i, b_i, c_i, d_i \leq 3^{30}

(a_i, b_i) \neq (c_i, d_i)

(a_i, b_i) and (c_i, d_i) are white squares.

All values in input are integers.

Input

Input is given from Standard Input in the following format:

Q
a_1 \ b_1 \ c_1 \ d_1
:
a_Q \ b_Q \ c_Q \ d_Q

Output

Print Q lines.
The i-th line should contain the distance from (a_i, b_i) to (c_i, d_i).

Sample Input 1

2
4 2 7 4
9 9 1 9

Sample Output 1

5
8

Solution in C++14 (GCC 5.4.1) (judge verdict: Wrong Answer)

#include <bits/stdc++.h>
using namespace std;

// template {{{
#define pb push_back
#define eb emplace_back
#define mp make_pair
#define mt make_tuple
#define lb lower_bound
#define ub upper_bound
#define f first
#define s second
#define resz resize

#define sz(x) int((x).size())
#define all(x) (x).begin(), (x).end()

#define FOR(i, a, b) for (int i = (a); i < (b); i++)
#define F0R(i, a) for (int i = 0; i < (a); i++)
#define FORd(i, a, b) for (int i = (b)-1; i >= (a); i--)
#define F0Rd(i, a) for (int i = (a)-1; i >= 0; i--)
#define trav(a, x) for (auto& a : x)

#define sort_by(x, y) sort(all(x), [&](const auto& a, const auto& b) { return y; })

using ll = long long;
using ld = long double;
using vi = vector<int>;
using vvi = vector<vi>;
using vll = vector<ll>;
using vvll = vector<vll>;
using vb = vector<bool>;
using vd = vector<double>;
using vs = vector<string>;

using pii = pair<int, int>;
using pll = pair<ll, ll>;
using pdd = pair<double, double>;

using vpii = vector<pii>;
using vvpii = vector<vpii>;
using vpll = vector<pll>;
using vvpll = vector<vpll>;
using vpdd = vector<pdd>;
using vvpdd = vector<vpdd>;

template<typename T> void ckmin(T& a, const T& b) { a = min(a, b); }
template<typename T> void ckmax(T& a, const T& b) { a = max(a, b); }

template<typename T> using max_heap = priority_queue<T>;
template<typename T> using min_heap = priority_queue<T, vector<T>, greater<T>>;

mt19937_64 rng(chrono::steady_clock::now().time_since_epoch().count());

namespace __input {
    template<class T1, class T2> void re(pair<T1,T2>& p);
    template<class T> void re(vector<T>& a);
    template<class T, size_t SZ> void re(array<T,SZ>& a);

    template<class T> void re(T& x) { cin >> x; }
    void re(double& x) { string t; re(t); x = stod(t); }
    template<class Arg, class... Args> void re(Arg& first, Args&... rest) {
        re(first); re(rest...);
    }

    template<class T1, class T2> void re(pair<T1,T2>& p) { re(p.f,p.s); }
    template<class T> void re(vector<T>& a) { F0R(i,sz(a)) re(a[i]); }
    template<class T, size_t SZ> void re(array<T,SZ>& a) { F0R(i,SZ) re(a[i]); }
}
using namespace __input;

namespace __output {
    template<class T1, class T2> void pr(const pair<T1,T2>& x);
    template<class T, size_t SZ> void pr(const array<T,SZ>& x);
    template<class T> void pr(const vector<T>& x);
    template<class T> void pr(const deque<T>& x);
    template<class T> void pr(const set<T>& x);
    template<class T1, class T2> void pr(const map<T1,T2>& x);

    template<class T> void pr(const T& x) { cout << x; }
    template<class Arg, class... Args> void pr(const Arg& first, const Args&... rest) {
        pr(first); pr(rest...);
    }

    template<class T1, class T2> void pr(const pair<T1,T2>& x) {
        pr("{",x.f,", ",x.s,"}");
    }
    template<class T, bool pretty = true> void prContain(const T& x) {
        if (pretty) pr("{");
        bool fst = 1; for (const auto& a: x) pr(!fst?pretty?", ":" ":"",a), fst = 0;
        if (pretty) pr("}");
    }
    template<class T> void pc(const T& x) { prContain<T, false>(x); pr("\n"); }
    template<class T, size_t SZ> void pr(const array<T,SZ>& x) { prContain(x); }
    template<class T> void pr(const vector<T>& x) { prContain(x); }
    template<class T> void pr(const deque<T>& x) { prContain(x); }
    template<class T> void pr(const set<T>& x) { prContain(x); }
    template<class T1, class T2> void pr(const map<T1,T2>& x) { prContain(x); }

    void ps() { pr("\n"); }
    template<class Arg> void ps(const Arg& first) {
        pr(first); ps();
    }
    template<class Arg, class... Args> void ps(const Arg& first, const Args&... rest) {
        pr(first," "); ps(rest...);
    }
}
using namespace __output;

#define TRACE(x) x
#define __pn(x) pr(#x, " = ")
#define pd(...) __pn((__VA_ARGS__)), ps(__VA_ARGS__), cout << flush

namespace __numeric {
    template<typename T>
    typename enable_if<is_integral<T>::value, T>::type floor(T n, T d) {
        assert(d != 0);
        if (d < 0) tie(n, d) = mp(-n, -d);
        return n / d - ((n < 0) && (n % d));
    }
    template<typename T>
    typename enable_if<is_integral<T>::value, T>::type ceil(T n, T d) {
        assert(d != 0);
        if (d < 0) tie(n, d) = mp(-n, -d);
        return n / d + ((n > 0) && (n % d));
    }
};
using namespace __numeric;

namespace __algorithm {
    template<typename T> void dedup(vector<T>& v) {
        sort(all(v)); v.erase(unique(all(v)), v.end());
    }
    template<typename T> typename vector<T>::iterator find(vector<T>& v, const T& x) {
        auto it = lower_bound(all(v), x); return it != v.end() && *it == x ? it : v.end();
    }
    template<typename T> size_t index(vector<T>& v, const T& x) {
        auto it = find(v, x); assert(it != v.end() && *it == x); return it - v.begin();
    }
    template<typename C, typename T, typename OP> vector<T> prefixes(const C& v, T id, OP op) {
        vector<T> r(sz(v)+1, id); F0R (i, sz(v)) r[i+1] = op(r[i], v[i]); return r;
    }
    template<typename C, typename T, typename OP> vector<T> suffixes(const C& v, T id, OP op) {
        vector<T> r(sz(v)+1, id); F0Rd (i, sz(v)) r[i] = op(v[i], r[i+1]); return r;
    }
}
using namespace __algorithm;

#pragma GCC diagnostic push
#pragma GCC diagnostic ignored "-Wunused-parameter"
struct monostate {
    friend istream& operator>>(istream& is, const monostate& ms) { return is; }
    friend ostream& operator<<(ostream& os, const monostate& ms) { return os; }
    friend monostate operator+(const monostate& a, const monostate& b) { return a; }
} ms;
#pragma GCC diagnostic pop

namespace __io {
    void setIn(string s) { freopen(s.c_str(),"r",stdin); }
    void setOut(string s) { freopen(s.c_str(),"w",stdout); }
    void setIO(string s = "") {
        ios_base::sync_with_stdio(0); cin.tie(0);
        cout << fixed << setprecision(15);
        if (sz(s)) { setIn(s+".in"), setOut(s+".out"); }
    }
}
using namespace __io;
// }}}

ll count(ll v) {
    return v/3 + ((v % 3) >= 1);
}

int main() {
    setIO();

    int Q; re(Q);

    F0R (q, Q) {
        ll a, b, c, d; re(a, b, c, d); --a, --b, --c, --d;

        ll straight = abs(a - c) + abs(b - d);
        ll add = 0;

        ll sz = 1;
        F0R (pw, 30) {
            ll A = a/sz, B = b/sz, C = c/sz, D = d/sz;
            //pd(A, B, C, D, sz);

            if (A == C && B != D && (((a % (3 * sz)) / sz) == 1)) {
                //pd(a, b, c, d, sz);
                ll betw = count(max(B, D)) - count(min(B, D));
                if (betw > 0) {
                    //pd(a, b, c, d, sz);

                    ll ar = a % sz, cr = c % sz;
                    //pd(ar, cr);
                    add = min(ar + cr + 2, 2 * sz - ar - cr);
                }
            }
            if (A != C && B == D && (((b % (3 * sz)) / sz) == 1)) {
                //pd(a, b, c, d, sz);
                ll betw = count(max(A, C)) - count(min(A, C));
                if (betw > 0) {
                    //pd(a, b, c, d, sz);

                    ll br = b % sz, dr = d % sz;
                    add = min(br + dr + 2, 2 * sz - br - dr);
                }
            }
            sz *= 3;
        }

        ps(straight + add);
    }

    // did you check N=1? did you mix up N,M?
    // check your "infinity" and "null" values against the bounds
    return 0;
}