#include <bits/stdc++.h>
using namespace std;
int main(int argc, char const *argv[]) {
  int t, n;
  cin >> t;
  vector<int> a;
  vector<int> f[2][2];
  vector<pair<int, int>> trace[2][2];
  while (t--) {
    cin >> n;
    a.resize(n);
    for (auto &u : a) cin >> u;
    for (int i = 0; i < 2; ++i)
      for (int j = 0; j < 2; ++j) {
        f[i][j].assign(n + 1, n + 1);
        trace[i][j].resize(n + 1);
      }
    f[0][0][0] = -n - 1;
    f[0][1][0] = -n - 1;
    for (int i = 0; i < n - 1; ++i) {
      if (f[0][0][i] <= n) {
        if (a[i + 1] > a[i])
          f[0][0][i + 1] = f[0][0][i], trace[0][0][i + 1] = {0, 0};
        else if (a[i + 1] > f[0][0][i])
          f[1][0][i + 1] = a[i], trace[1][0][i + 1] = {0, 0};
        if (-a[i + 1] > f[0][0][i])
          f[1][1][i + 1] = a[i], trace[1][1][i + 1] = {0, 0};
      }
      if (f[0][1][i] <= n) {
        if (f[0][1][i] < f[0][0][i + 1])
          f[0][0][i + 1] = f[0][1][i], trace[0][0][i + 1] = {0, 1};
        if (a[i + 1] < a[i])
          f[0][1][i + 1] = f[0][1][i], trace[0][1][i + 1] = {0, 1};
        else if (-a[i + 1] > f[0][1][i])
          f[1][1][i + 1] = -a[i], trace[1][1][i + 1] = {0, 1};
      }
      if (f[1][0][i] <= n) {
        if (a[i + 1] > f[1][0][i] && f[0][0][i + 1] > a[i])
          f[0][0][i + 1] = a[i], trace[0][0][i + 1] = {1, 0};
        else if (a[i + 1] > a[i] && f[1][0][i + 1] > f[1][0][i])
          f[1][0][i + 1] = f[1][0][i], trace[1][0][i + 1] = {1, 0};
      }
      if (f[1][1][i] <= n) {
        if (a[i + 1] > f[1][1][i] && f[0][0][i + 1] > -a[i])
          f[0][0][i + 1] = -a[i], trace[0][0][i + 1] = {1, 1};
        else if (f[1][0][i + 1] > f[1][1][i])
          f[1][0][i + 1] = f[1][1][i], trace[1][0][i + 1] = {1, 1};
        if (-a[i + 1] > f[1][1][i] && f[0][1][i + 1] > -a[i])
          f[0][1][i + 1] = -a[i], trace[0][1][i + 1] = {1, 1};
        else if (a[i + 1] < a[i] && f[1][1][i + 1] > f[1][1][i])
          f[1][1][i + 1] = f[1][1][i], trace[1][1][i + 1] = {1, 1};
      }
    }
    pair<int, int> res{-1, -1};
    for (int i = 0; i < 2; ++i)
      for (int j = 0; j < 2; ++j)
        if (f[i][j][n - 1] <= n) res = {i, j};
    if (res.first == -1) {
      cout << "NO" << endl;
      continue;
    }
    cout << "YES" << endl;
    vector<int> ans;
    for (int i = n - 1; i >= 0; --i) {
      ans.push_back(res.second ? -a[i] : a[i]);
      res = trace[res.first][res.second][i];
    }
    for (auto it = ans.rbegin(); it != ans.rend(); ++it) cout << *it << " ";
    cout << endl;
  }
  return 0;
}

### Prompt

Please provide a cpp coded solution to the problem described below:

You are given a permutation p consisting of n integers 1, 2, ..., n (a permutation is an array where each element from 1 to n occurs exactly once).

Let's call an array a bipartite if the following undirected graph is bipartite:

  * the graph consists of n vertices; 
  * two vertices i and j are connected by an edge if i < j and a_i > a_j. 



Your task is to find a bipartite array of integers a of size n, such that a_i = p_i or a_i = -p_i, or report that no such array exists. If there are multiple answers, print any of them.

Input

The first line contains a single integer t (1 ≤ t ≤ 2 ⋅ 10^5) — the number of test cases.

The first line of each test case contains a single integer n (1 ≤ n ≤ 10^6) — the size of the permutation.

The second line contains n integers p_1, p_2, ..., p_n.

The sum of n over all test cases doesn't exceed 10^6.

Output

For each test case, print the answer in the following format. If such an array a does not exist, print "NO" in a single line. Otherwise, print "YES" in the first line and n integers — array a in the second line.

Example

Input


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


Output


YES
1 2 3
NO
YES
-4 -1 -3 -2
YES
-3 -2 1 6 7 -8 -5 -4

### Response

```cpp
#include <bits/stdc++.h>
using namespace std;
int main(int argc, char const *argv[]) {
  int t, n;
  cin >> t;
  vector<int> a;
  vector<int> f[2][2];
  vector<pair<int, int>> trace[2][2];
  while (t--) {
    cin >> n;
    a.resize(n);
    for (auto &u : a) cin >> u;
    for (int i = 0; i < 2; ++i)
      for (int j = 0; j < 2; ++j) {
        f[i][j].assign(n + 1, n + 1);
        trace[i][j].resize(n + 1);
      }
    f[0][0][0] = -n - 1;
    f[0][1][0] = -n - 1;
    for (int i = 0; i < n - 1; ++i) {
      if (f[0][0][i] <= n) {
        if (a[i + 1] > a[i])
          f[0][0][i + 1] = f[0][0][i], trace[0][0][i + 1] = {0, 0};
        else if (a[i + 1] > f[0][0][i])
          f[1][0][i + 1] = a[i], trace[1][0][i + 1] = {0, 0};
        if (-a[i + 1] > f[0][0][i])
          f[1][1][i + 1] = a[i], trace[1][1][i + 1] = {0, 0};
      }
      if (f[0][1][i] <= n) {
        if (f[0][1][i] < f[0][0][i + 1])
          f[0][0][i + 1] = f[0][1][i], trace[0][0][i + 1] = {0, 1};
        if (a[i + 1] < a[i])
          f[0][1][i + 1] = f[0][1][i], trace[0][1][i + 1] = {0, 1};
        else if (-a[i + 1] > f[0][1][i])
          f[1][1][i + 1] = -a[i], trace[1][1][i + 1] = {0, 1};
      }
      if (f[1][0][i] <= n) {
        if (a[i + 1] > f[1][0][i] && f[0][0][i + 1] > a[i])
          f[0][0][i + 1] = a[i], trace[0][0][i + 1] = {1, 0};
        else if (a[i + 1] > a[i] && f[1][0][i + 1] > f[1][0][i])
          f[1][0][i + 1] = f[1][0][i], trace[1][0][i + 1] = {1, 0};
      }
      if (f[1][1][i] <= n) {
        if (a[i + 1] > f[1][1][i] && f[0][0][i + 1] > -a[i])
          f[0][0][i + 1] = -a[i], trace[0][0][i + 1] = {1, 1};
        else if (f[1][0][i + 1] > f[1][1][i])
          f[1][0][i + 1] = f[1][1][i], trace[1][0][i + 1] = {1, 1};
        if (-a[i + 1] > f[1][1][i] && f[0][1][i + 1] > -a[i])
          f[0][1][i + 1] = -a[i], trace[0][1][i + 1] = {1, 1};
        else if (a[i + 1] < a[i] && f[1][1][i + 1] > f[1][1][i])
          f[1][1][i + 1] = f[1][1][i], trace[1][1][i + 1] = {1, 1};
      }
    }
    pair<int, int> res{-1, -1};
    for (int i = 0; i < 2; ++i)
      for (int j = 0; j < 2; ++j)
        if (f[i][j][n - 1] <= n) res = {i, j};
    if (res.first == -1) {
      cout << "NO" << endl;
      continue;
    }
    cout << "YES" << endl;
    vector<int> ans;
    for (int i = n - 1; i >= 0; --i) {
      ans.push_back(res.second ? -a[i] : a[i]);
      res = trace[res.first][res.second][i];
    }
    for (auto it = ans.rbegin(); it != ans.rend(); ++it) cout << *it << " ";
    cout << endl;
  }
  return 0;
}

```