AquaMoon has n friends. They stand in a row from left to right, and the i-th friend from the left wears a T-shirt with a number a_i written on it. Each friend has a direction (left or right). In the beginning, the direction of each friend is right.

AquaMoon can make some operations on friends. On each operation, AquaMoon can choose two adjacent friends and swap their positions. After each operation, the direction of both chosen friends will also be flipped: left to right and vice versa.

AquaMoon hopes that after some operations, the numbers written on the T-shirt of n friends in the row, read from left to right, become non-decreasing. Also she wants, that all friends will have a direction of right at the end. Please find if it is possible.

Input

The input consists of multiple test cases. The first line contains a single integer t (1 ≤ t ≤ 50) — the number of test cases.

The first line of each test case contains a single integer n (1 ≤ n ≤ 10^5) — the number of Aquamoon's friends.

The second line contains n integers a_1, a_2, ..., a_n (1 ≤ a_i ≤ 10^5) — the numbers, written on the T-shirts.

It is guaranteed that the sum of n for all test cases does not exceed 10^5.

Output

For each test case, if there exists a possible sequence of operations, print "YES" (without quotes); otherwise, print "NO" (without quotes).

You can print each letter in any case (upper or lower).

Example

Input


3
4
4 3 2 5
4
3 3 2 2
5
1 2 3 5 4


Output


YES
YES
NO

Note

The possible list of operations in the first test case:

  1. Swap a_1 and a_2. The resulting sequence is 3, 4, 2, 5. The directions are: left, left, right, right. 
  2. Swap a_2 and a_3. The resulting sequence is 3, 2, 4, 5. The directions are: left, left, right, right. 
  3. Swap a_1 and a_2. The resulting sequence is 2, 3, 4, 5. The directions are: right, right, right, right. 
 #include <bits/stdc++.h>
using namespace std;

// clang-format off
// template {{{
#define pb push_back
#define eb emplace_back
#define mp make_pair
#define f first
#define s second

#define sz(x) int((x).size())
#define all(x) (x).begin(), (x).end()
#define rall(x) (x).rbegin(), (x).rend()
#define trav(a, x) for (auto &a : x)

#define L1(u, ...) [&](auto &&u) { return __VA_ARGS__; }
#define L2(u, v, ...) [&](auto &&u, auto &&v) { return __VA_ARGS__; }

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

using ll = long long;
using vi = vector<int>;
using vvi = vector<vi>;
using vll = vector<ll>;
using vvll = vector<vll>;
using vb = vector<bool>;
using vvb = vector<vb>;
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 vpll = vector<pll>;
using vpdd = vector<pdd>;

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); }

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.first, p.second); }
    template <class T> void re(vector<T> &a) { for (auto &x : a) re(x); }
    template <class T, size_t SZ> void re(array<T, SZ> &a) { for (auto &x : a) re(x); }
}
using namespace __input;

namespace __output {
    template <typename T> struct is_outputtable { template <typename C> static constexpr decltype(declval<ostream &>() << declval<const C &>(), bool()) test(int) { return true; } template <typename C> static constexpr bool test(...) { return false; } static constexpr bool value = test<T>(int()); };
    template <class T, typename V = decltype(declval<const T &>().begin()), typename S = typename enable_if<!is_outputtable<T>::value, bool>::type> void pr(const T &x);

    template <class T, typename V = decltype(declval<ostream &>() << declval<const T &>())> void pr(const T &x) { cout << x; }
    template <class T1, class T2> void pr(const pair<T1, T2> &x);
    template <class Arg, class... Args> void pr(const Arg &first, const Args &...rest) { pr(first); pr(rest...); }

    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 T1, class T2> void pr(const pair<T1, T2> &x) { pr("{", x.first, ", ", x.second, "}"); }
    template <class T, typename V, typename S> void pr(const T &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 __pn(x) pr(#x, " = ")
#ifdef PRIME_DEBUG
#define pd(...) pr("\033[1;31m"), __pn((__VA_ARGS__)), ps(__VA_ARGS__), pr("\033[0m"), cout << flush
#else
#define pd(...)
#endif

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>::const_iterator find(const 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(const vector<T> &v, const T &x) { auto it = find(v, x); assert(it != v.end() && *it == x); return it - v.begin(); }
    template <typename I> struct _reversed_struct { I &v_; explicit _reversed_struct(I &v) : v_{v} {} typename I::reverse_iterator begin() const { return v_.rbegin(); } typename I::reverse_iterator end() const { return v_.rend(); } };
    template <typename I> _reversed_struct<I> reversed(I &v) { return _reversed_struct<I>(v); }
}
using namespace __algorithm;

namespace __io {
    void setIO() { ios_base::sync_with_stdio(0); cin.tie(0); cout << setprecision(15); }
}
using namespace __io;
// }}}

// clang-format on

const int INF = 2e9;

void solve() {
    int n;re(n);
    vi a(n);vector<vector<int>> b(1e5+1,vi(2));

    for(int i=0;i<n;i++)
    {
    	cin >> a[i];
    	b[a[i]][i%2]++;
    }
    bool pass = true;
    sort(a.begin(),a.end());
    for(int i=0;i<n;i++)
    {
    	if(b[a[i]][i%2]==0)
    		pass=false;
    	else b[a[i]][i%2]--;
    }
    cout << (pass ? "YES" : "NO") << endl;
}

int main() {
    setIO();

    int T;
    re(T);
    for (int t = 0; t < T; t++)
        solve();

    return 0;
}
