/*
    author:  Maksim1744
    created: 28.05.2021 19:09:05
*/

#include "bits/stdc++.h"

using namespace std;

using ll = long long;
using ld = long double;

#define mp   make_pair
#define pb   push_back
#define eb   emplace_back

#define sum(a)     ( accumulate ((a).begin(), (a).end(), 0ll))
#define mine(a)    (*min_element((a).begin(), (a).end()))
#define maxe(a)    (*max_element((a).begin(), (a).end()))
#define mini(a)    ( min_element((a).begin(), (a).end()) - (a).begin())
#define maxi(a)    ( max_element((a).begin(), (a).end()) - (a).begin())
#define lowb(a, x) ( lower_bound((a).begin(), (a).end(), (x)) - (a).begin())
#define uppb(a, x) ( upper_bound((a).begin(), (a).end(), (x)) - (a).begin())

template<typename T>             vector<T>& operator--            (vector<T> &v){for (auto& i : v) --i;            return  v;}
template<typename T>             vector<T>& operator++            (vector<T> &v){for (auto& i : v) ++i;            return  v;}
template<typename T>             istream& operator>>(istream& is,  vector<T> &v){for (auto& i : v) is >> i;        return is;}
template<typename T>             ostream& operator<<(ostream& os,  vector<T>  v){for (auto& i : v) os << i << ' '; return os;}
template<typename T, typename U> pair<T,U>& operator--           (pair<T, U> &p){--p.first; --p.second;            return  p;}
template<typename T, typename U> pair<T,U>& operator++           (pair<T, U> &p){++p.first; ++p.second;            return  p;}
template<typename T, typename U> istream& operator>>(istream& is, pair<T, U> &p){is >> p.first >> p.second;        return is;}
template<typename T, typename U> ostream& operator<<(ostream& os, pair<T, U>  p){os << p.first << ' ' << p.second; return os;}
template<typename T, typename U> pair<T,U> operator-(pair<T,U> a, pair<T,U> b){return mp(a.first-b.first, a.second-b.second);}
template<typename T, typename U> pair<T,U> operator+(pair<T,U> a, pair<T,U> b){return mp(a.first+b.first, a.second+b.second);}
template<typename T, typename U> void umin(T& a, U b){if (a > b) a = b;}
template<typename T, typename U> void umax(T& a, U b){if (a < b) a = b;}

#ifdef HOME
#define SHOW_COLORS
#include "C:/C++ libs/print.cpp"
#else
#define show(...) void(0)
#define mclock    void(0)
#define shows     void(0)
#define debug  if (false)
#endif

#ifdef HOUSE
mt19937_64 rng(1283792);
#else
mt19937_64 rng(chrono::steady_clock::now().time_since_epoch().count());
#endif
ll rnd (ll l, ll r) { return (ll)(rng() % (r - l + 1)) + l; }
ll rnd (ll r)       { return rng() % r; }
ll rnd ()           { return rng(); }
ld rndf()           { return (ld)rng() / (ld)ULLONG_MAX; }
ld rndf(ld l, ld r) { return rndf() * (r - l) + l; }

void test_case(int test) {
    int n;
    cin >> n;
    int q = 0;
    auto ask = [&](int a, int b, int c) {
        ++q;
        cout << "? " << a + 1 << ' ' << b + 1 << ' ' << c + 1 << endl;
        int k;
        cin >> k;
        if (k == -1) exit(0);
        return k;
    };

    int l = -1, r = -1;
    int its = 0;
    while (true) {
        assert(its < 100);
        vector<int> v;
        while (v.size() < 4) {
            v.pb(rnd(n));
            sort(v.begin(), v.end());
            v.erase(unique(v.begin(), v.end()), v.end());
        }

        vector<pair<int, int>> best;
        for (int i = 0; i < 4; ++i) {
            vector<int> u;
            for (int j = 0; j < 4; ++j) {
                if (i != j)
                    u.pb(v[j]);
            }
            int a = u[0], b = u[1], c = u[2];
            best.eb(ask(a, b, c), i);
        }
        sort(best.begin(), best.end());
        set<int> s;
        for (auto p : best)
            s.insert(p.first);
        if (s.size() != 4) continue;
        if (*prev(s.end()) >= 4) {
            vector<int> u;
            for (int i = 0; i < 4; ++i) {
                if (i != best[2].second && i != best[3].second)
                    u.pb(i);
            }
            assert(u.size() == 2);
            l = v[u[0]];
            r = v[u[1]];
            break;
        }
    }

    show(l, r);

    vector<int> resp(n, 1e9);
    for (int i = 0; i < n; ++i) {
        if (i == l || i == r) continue;
        resp[i] = ask(i, l, r);
    }
    show(resp);
    int mn = mine(resp);
    int dist = mn * 2;
    if (count(resp.begin(), resp.end(), mn) == 2) --dist;
    map<int, int> pos;
    pos[l] = 0;
    pos[r] = dist;
    int mid;
    if (count(resp.begin(), resp.end(), mn) == 2) {
        int a = -1, b = -1;
        for (int i = 0; i < n; ++i) {
            if (resp[i] == mn) {
                if (a == -1) a = i;
                else b = i;
            }
        }
        int na = -1, nb = -1;
        for (int i = 0; i < n; ++i) {
            if (resp[i] == mn + 1) {
                if (na == -1) na = i;
                else nb = i;
            }
        }
        // int r1 = max(ask(l, a, na), ask(l, a, nb));
        int r2 = max(ask(l, b, na), ask(l, b, nb));
        show(a, b);
        show(na, nb);
        show(r2);
        if (r2 == dist / 2)
            swap(a, b);
        pos[a] = dist / 2;
        pos[b] = pos[a] + 1;
        mid = a;
    } else {
        pos[mini(resp)] = dist / 2;
        mid = mini(resp);
    }

    show(mid);
    show(dist);
    show(pos);
    show(l, r);

    for (int i = 0; i < n; ++i) {
        if (resp[i] < dist && !pos.count(i)) {
            int d = ask(l, mid, i);
            show(i, d);
            if (d < dist / 2) {
                pos[i] = dist - resp[i];
            } else {
                pos[i] = resp[i];
            }
        }
    }
    show(pos);
    int nl = -1;
    for (auto [a, b] : pos)
        if (b == 1)
            nl = a;
    show(nl);
    assert(nl != -1);
    for (int i = 0; i < n; ++i) {
        if (resp[i] == dist && !pos.count(i)) {
            int d = ask(l, nl, i);
            show(i, d);
            if (d == dist) continue;
            if (d < dist) {
                pos[i] = -d;
            } else {
                pos[i] = 1 + d;
            }
        }
    }
    show(pos);
    int nr = -1;
    for (auto [a, b] : pos)
        if (b == dist - 1)
            nr = a;
    show(nr);
    assert(nr != -1);
    for (int i = 0; i < n; ++i) {
        if (resp[i] == dist && !pos.count(i)) {
            int d = ask(r, nr, i);
            if (d == dist) continue;
            if (d < dist) {
                pos[i] = dist + d;
            } else {
                pos[i] = dist - 1 - d;
            }
        }
    }
    show(pos);

    for (int i = 0; i < n; ++i) {
        if (resp[i] > dist && !pos.count(i)) {
            int d = ask(l, nl, i);
            if (d == resp[i]) {
                pos[i] = -d;
            } else {
                pos[i] = 1 + d;
            }
        }
    }
    show(pos);
    int fr = 1e9;
    for (auto [a, b] : pos)
        fr = min(fr, b);
    vector<int> p(n, -1);
    for (auto [a, b] : pos)
        p[a] = b - fr;
    if (p[0] > p[1]) {
        for (int i = 0; i < n; ++i) {
            p[i] = n - 1 - p[i];
        }
    }
    ++p;
    cout << "! " << p << endl;
    show(p);
    cerr << q << endl;
    cin >> n;
}

int main() {
    ios_base::sync_with_stdio(false); cin.tie(NULL); cout.tie(NULL);

    int T;
    cin >> T;
    for (int test = 1; test <= T; ++test) {
        test_case(test);
    }

    return 0;
}

### Prompt

In CPP, your task is to solve the following problem:

This is an interactive problem.

There is a secret permutation p (1-indexed) of numbers from 1 to n. More formally, for 1 ≤ i ≤ n, 1 ≤ p[i] ≤ n and for 1 ≤ i < j ≤ n, p[i] ≠ p[j]. It is known that p[1]<p[2].

In 1 query, you give 3 distinct integers a,b,c (1 ≤ a,b,c ≤ n), and receive the median of \{|p[a]-p[b]|,|p[b]-p[c]|,|p[a]-p[c]|\}.

In this case, the median is the 2-nd element (1-indexed) of the sequence when sorted in non-decreasing order. The median of \{4,6,2\} is 4 and the median of \{0,123,33\} is 33.

Can you find the secret permutation in not more than 2n+420 queries?

Note: the grader is not adaptive: the permutation is fixed before any queries are made.

Input

The first line of input contains a single integer t (1 ≤ t ≤ 1000) — the number of testcases.

The first line of each testcase consists of a single integer n (20 ≤ n ≤ 100000) — the length of the secret permutation.

It is guaranteed that the sum of n over all test cases does not exceed 100000.

Interaction

For each testcase, you begin the interaction by reading n.

To perform a query, output "? a b c" where a,b,c is the 3 indices you want to use for the query.

Numbers have to satisfy 1 ≤ a,b,c ≤ n and a ≠ b,b ≠ c,a ≠ c.

For each query, you will receive a single integer x: the median of \{|p[a]-p[b]|,|p[b]-p[c]|,|p[a]-p[c]|\}.

In case your query is invalid or you asked more than 2n+420 queries, the interactor will print "−1" and will finish interaction. You will receive Wrong answer verdict. Make sure to exit immediately to avoid getting other verdicts.

When you have determined the secret permutation, output "! p[1] p[2] ... p[n]". If the secret permutation is correct, the interactor will print "1". Otherwise, the interactor will print "-1" and will finish interaction. You will receive Wrong answer verdict. Make sure to exit immediately to avoid getting other verdicts.

After printing a query do not forget to output the end of line and flush the output. Otherwise, you will get Idleness limit exceeded verdict.

To do this, use:

  * fflush(stdout) or cout.flush() in C++;
  * System.out.flush() in Java;
  * flush(output) in Pascal;
  * stdout.flush() in Python;
  * see documentation for other languages.



Hacks:

To hack, use the following format of test:

The first line should contain a single integer t (1 ≤ t ≤ 1000) — the number of testcases.

The first line of each testcase should contain a single integer n (20 ≤ n ≤ 100000) — the length of the secret permutation.

The following line of should contain n integers p[1],p[2],p[3],…,p[n]. p[1]<p[2] and p must be a permutation of integers from 1 to n.

You must ensure that the sum of n over all testcases does not exceed 100000.

Example

Input


1
20

6

9

1

Output




? 1 5 2

? 20 19 2

! 9 10 19 7 16 18 11 14 15 6 20 8 17 4 5 3 12 2 13 1

Note

The secret permutation is \{9,10,19,7,16,18,11,14,15,6,20,8,17,4,5,3,12,2,13,1\}.

For the first query, the values of (a,b,c) is (1,5,2). Since p[1]=9, p[5]=16 and p[2]=10. The return value is the median of \{|9-16|,|16-10|,|9-10|\} which is 6.

For the second query, the values of (a,b,c) is (20,19,2). Since p[20]=1, p[19]=13 and p[2]=10. The return value is the median of \{|1-13|,|13-10|,|1-10|\} which is 9.

By some miracle, we have figured out that the secret permutation is \{9,10,19,7,16,18,11,14,15,6,20,8,17,4,5,3,12,2,13,1\}. We output it and receive 1 from the interactor, meaning that we have guessed the secret permutation correctly.

### Response

```cpp
/*
    author:  Maksim1744
    created: 28.05.2021 19:09:05
*/

#include "bits/stdc++.h"

using namespace std;

using ll = long long;
using ld = long double;

#define mp   make_pair
#define pb   push_back
#define eb   emplace_back

#define sum(a)     ( accumulate ((a).begin(), (a).end(), 0ll))
#define mine(a)    (*min_element((a).begin(), (a).end()))
#define maxe(a)    (*max_element((a).begin(), (a).end()))
#define mini(a)    ( min_element((a).begin(), (a).end()) - (a).begin())
#define maxi(a)    ( max_element((a).begin(), (a).end()) - (a).begin())
#define lowb(a, x) ( lower_bound((a).begin(), (a).end(), (x)) - (a).begin())
#define uppb(a, x) ( upper_bound((a).begin(), (a).end(), (x)) - (a).begin())

template<typename T>             vector<T>& operator--            (vector<T> &v){for (auto& i : v) --i;            return  v;}
template<typename T>             vector<T>& operator++            (vector<T> &v){for (auto& i : v) ++i;            return  v;}
template<typename T>             istream& operator>>(istream& is,  vector<T> &v){for (auto& i : v) is >> i;        return is;}
template<typename T>             ostream& operator<<(ostream& os,  vector<T>  v){for (auto& i : v) os << i << ' '; return os;}
template<typename T, typename U> pair<T,U>& operator--           (pair<T, U> &p){--p.first; --p.second;            return  p;}
template<typename T, typename U> pair<T,U>& operator++           (pair<T, U> &p){++p.first; ++p.second;            return  p;}
template<typename T, typename U> istream& operator>>(istream& is, pair<T, U> &p){is >> p.first >> p.second;        return is;}
template<typename T, typename U> ostream& operator<<(ostream& os, pair<T, U>  p){os << p.first << ' ' << p.second; return os;}
template<typename T, typename U> pair<T,U> operator-(pair<T,U> a, pair<T,U> b){return mp(a.first-b.first, a.second-b.second);}
template<typename T, typename U> pair<T,U> operator+(pair<T,U> a, pair<T,U> b){return mp(a.first+b.first, a.second+b.second);}
template<typename T, typename U> void umin(T& a, U b){if (a > b) a = b;}
template<typename T, typename U> void umax(T& a, U b){if (a < b) a = b;}

#ifdef HOME
#define SHOW_COLORS
#include "C:/C++ libs/print.cpp"
#else
#define show(...) void(0)
#define mclock    void(0)
#define shows     void(0)
#define debug  if (false)
#endif

#ifdef HOUSE
mt19937_64 rng(1283792);
#else
mt19937_64 rng(chrono::steady_clock::now().time_since_epoch().count());
#endif
ll rnd (ll l, ll r) { return (ll)(rng() % (r - l + 1)) + l; }
ll rnd (ll r)       { return rng() % r; }
ll rnd ()           { return rng(); }
ld rndf()           { return (ld)rng() / (ld)ULLONG_MAX; }
ld rndf(ld l, ld r) { return rndf() * (r - l) + l; }

void test_case(int test) {
    int n;
    cin >> n;
    int q = 0;
    auto ask = [&](int a, int b, int c) {
        ++q;
        cout << "? " << a + 1 << ' ' << b + 1 << ' ' << c + 1 << endl;
        int k;
        cin >> k;
        if (k == -1) exit(0);
        return k;
    };

    int l = -1, r = -1;
    int its = 0;
    while (true) {
        assert(its < 100);
        vector<int> v;
        while (v.size() < 4) {
            v.pb(rnd(n));
            sort(v.begin(), v.end());
            v.erase(unique(v.begin(), v.end()), v.end());
        }

        vector<pair<int, int>> best;
        for (int i = 0; i < 4; ++i) {
            vector<int> u;
            for (int j = 0; j < 4; ++j) {
                if (i != j)
                    u.pb(v[j]);
            }
            int a = u[0], b = u[1], c = u[2];
            best.eb(ask(a, b, c), i);
        }
        sort(best.begin(), best.end());
        set<int> s;
        for (auto p : best)
            s.insert(p.first);
        if (s.size() != 4) continue;
        if (*prev(s.end()) >= 4) {
            vector<int> u;
            for (int i = 0; i < 4; ++i) {
                if (i != best[2].second && i != best[3].second)
                    u.pb(i);
            }
            assert(u.size() == 2);
            l = v[u[0]];
            r = v[u[1]];
            break;
        }
    }

    show(l, r);

    vector<int> resp(n, 1e9);
    for (int i = 0; i < n; ++i) {
        if (i == l || i == r) continue;
        resp[i] = ask(i, l, r);
    }
    show(resp);
    int mn = mine(resp);
    int dist = mn * 2;
    if (count(resp.begin(), resp.end(), mn) == 2) --dist;
    map<int, int> pos;
    pos[l] = 0;
    pos[r] = dist;
    int mid;
    if (count(resp.begin(), resp.end(), mn) == 2) {
        int a = -1, b = -1;
        for (int i = 0; i < n; ++i) {
            if (resp[i] == mn) {
                if (a == -1) a = i;
                else b = i;
            }
        }
        int na = -1, nb = -1;
        for (int i = 0; i < n; ++i) {
            if (resp[i] == mn + 1) {
                if (na == -1) na = i;
                else nb = i;
            }
        }
        // int r1 = max(ask(l, a, na), ask(l, a, nb));
        int r2 = max(ask(l, b, na), ask(l, b, nb));
        show(a, b);
        show(na, nb);
        show(r2);
        if (r2 == dist / 2)
            swap(a, b);
        pos[a] = dist / 2;
        pos[b] = pos[a] + 1;
        mid = a;
    } else {
        pos[mini(resp)] = dist / 2;
        mid = mini(resp);
    }

    show(mid);
    show(dist);
    show(pos);
    show(l, r);

    for (int i = 0; i < n; ++i) {
        if (resp[i] < dist && !pos.count(i)) {
            int d = ask(l, mid, i);
            show(i, d);
            if (d < dist / 2) {
                pos[i] = dist - resp[i];
            } else {
                pos[i] = resp[i];
            }
        }
    }
    show(pos);
    int nl = -1;
    for (auto [a, b] : pos)
        if (b == 1)
            nl = a;
    show(nl);
    assert(nl != -1);
    for (int i = 0; i < n; ++i) {
        if (resp[i] == dist && !pos.count(i)) {
            int d = ask(l, nl, i);
            show(i, d);
            if (d == dist) continue;
            if (d < dist) {
                pos[i] = -d;
            } else {
                pos[i] = 1 + d;
            }
        }
    }
    show(pos);
    int nr = -1;
    for (auto [a, b] : pos)
        if (b == dist - 1)
            nr = a;
    show(nr);
    assert(nr != -1);
    for (int i = 0; i < n; ++i) {
        if (resp[i] == dist && !pos.count(i)) {
            int d = ask(r, nr, i);
            if (d == dist) continue;
            if (d < dist) {
                pos[i] = dist + d;
            } else {
                pos[i] = dist - 1 - d;
            }
        }
    }
    show(pos);

    for (int i = 0; i < n; ++i) {
        if (resp[i] > dist && !pos.count(i)) {
            int d = ask(l, nl, i);
            if (d == resp[i]) {
                pos[i] = -d;
            } else {
                pos[i] = 1 + d;
            }
        }
    }
    show(pos);
    int fr = 1e9;
    for (auto [a, b] : pos)
        fr = min(fr, b);
    vector<int> p(n, -1);
    for (auto [a, b] : pos)
        p[a] = b - fr;
    if (p[0] > p[1]) {
        for (int i = 0; i < n; ++i) {
            p[i] = n - 1 - p[i];
        }
    }
    ++p;
    cout << "! " << p << endl;
    show(p);
    cerr << q << endl;
    cin >> n;
}

int main() {
    ios_base::sync_with_stdio(false); cin.tie(NULL); cout.tie(NULL);

    int T;
    cin >> T;
    for (int test = 1; test <= T; ++test) {
        test_case(test);
    }

    return 0;
}

```