#include <bits/stdc++.h>
using namespace std;
int n, p[1000100];
int dp[1000100][2][2];
pair<bool, bool> pre[1000100][2][2];
void dfs(int u, int x, int y) {
  if (u == n + 1) return;
  cout << (!x ? -p[u] : p[u]) << ' ';
  dfs(u + 1, pre[u][x][y].first, pre[u][x][y].second);
}
void Solve() {
  cin >> n;
  for (int i = 1; i <= n; ++i) {
    cin >> p[i];
    dp[i][0][0] = dp[i][0][1] = dp[i][1][0] = dp[i][1][1] = -n - 1;
  }
  dp[n][0][0] = dp[n][1][0] = n + 1;
  for (int i = n - 1; i >= 1; --i) {
    for (int c = 0; c < 2; ++c) {
      int z = !c ? -p[i] : p[i];
      if (dp[i + 1][0][0] >= -n) {
        int x = -p[i + 1], y = dp[i + 1][0][0];
        if (z < x) {
          if (y > dp[i][c][0]) {
            dp[i][c][0] = y, pre[i][c][0] = pair<bool, bool>(0, 0);
          }
        } else if (z < y) {
          if (x > dp[i][c][1]) {
            dp[i][c][1] = x, pre[i][c][1] = pair<bool, bool>(0, 0);
          }
        }
      }
      if (dp[i + 1][1][0] >= -n) {
        int x = p[i + 1], y = dp[i + 1][1][0];
        if (z < x) {
          if (y > dp[i][c][0]) {
            dp[i][c][0] = y, pre[i][c][0] = pair<bool, bool>(1, 0);
          }
        } else if (z < y) {
          if (x > dp[i][c][1]) {
            dp[i][c][1] = x, pre[i][c][1] = pair<bool, bool>(1, 0);
          }
        }
      }
      if (dp[i + 1][0][1] >= -n) {
        int y = -p[i + 1], x = dp[i + 1][0][1];
        if (z < x) {
          if (y > dp[i][c][0]) {
            dp[i][c][0] = y, pre[i][c][0] = pair<bool, bool>(0, 1);
          }
        } else if (z < y) {
          if (x > dp[i][c][1]) {
            dp[i][c][1] = x, pre[i][c][1] = pair<bool, bool>(0, 1);
          }
        }
      }
      if (dp[i + 1][1][1] >= -n) {
        int y = p[i + 1], x = dp[i + 1][1][1];
        if (z < x) {
          if (y > dp[i][c][0]) {
            dp[i][c][0] = y, pre[i][c][0] = pair<bool, bool>(1, 1);
          }
        } else if (z < y) {
          if (x > dp[i][c][1]) {
            dp[i][c][1] = x, pre[i][c][1] = pair<bool, bool>(1, 1);
          }
        }
      }
    }
  }
  for (int i = 0; i < 2; ++i) {
    for (int j = 0; j < 2; ++j) {
      if (dp[1][i][j] >= -n) {
        cout << "YES\n";
        dfs(1, i, j);
        cout << '\n';
        return;
      }
    }
  }
  cout << "NO\n";
}
int main() {
  ios::sync_with_stdio(false);
  cin.tie(0);
  int T;
  cin >> T;
  while (T--) Solve();
  return 0;
}

### Prompt

Create a solution in cpp for the following problem:

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 n, p[1000100];
int dp[1000100][2][2];
pair<bool, bool> pre[1000100][2][2];
void dfs(int u, int x, int y) {
  if (u == n + 1) return;
  cout << (!x ? -p[u] : p[u]) << ' ';
  dfs(u + 1, pre[u][x][y].first, pre[u][x][y].second);
}
void Solve() {
  cin >> n;
  for (int i = 1; i <= n; ++i) {
    cin >> p[i];
    dp[i][0][0] = dp[i][0][1] = dp[i][1][0] = dp[i][1][1] = -n - 1;
  }
  dp[n][0][0] = dp[n][1][0] = n + 1;
  for (int i = n - 1; i >= 1; --i) {
    for (int c = 0; c < 2; ++c) {
      int z = !c ? -p[i] : p[i];
      if (dp[i + 1][0][0] >= -n) {
        int x = -p[i + 1], y = dp[i + 1][0][0];
        if (z < x) {
          if (y > dp[i][c][0]) {
            dp[i][c][0] = y, pre[i][c][0] = pair<bool, bool>(0, 0);
          }
        } else if (z < y) {
          if (x > dp[i][c][1]) {
            dp[i][c][1] = x, pre[i][c][1] = pair<bool, bool>(0, 0);
          }
        }
      }
      if (dp[i + 1][1][0] >= -n) {
        int x = p[i + 1], y = dp[i + 1][1][0];
        if (z < x) {
          if (y > dp[i][c][0]) {
            dp[i][c][0] = y, pre[i][c][0] = pair<bool, bool>(1, 0);
          }
        } else if (z < y) {
          if (x > dp[i][c][1]) {
            dp[i][c][1] = x, pre[i][c][1] = pair<bool, bool>(1, 0);
          }
        }
      }
      if (dp[i + 1][0][1] >= -n) {
        int y = -p[i + 1], x = dp[i + 1][0][1];
        if (z < x) {
          if (y > dp[i][c][0]) {
            dp[i][c][0] = y, pre[i][c][0] = pair<bool, bool>(0, 1);
          }
        } else if (z < y) {
          if (x > dp[i][c][1]) {
            dp[i][c][1] = x, pre[i][c][1] = pair<bool, bool>(0, 1);
          }
        }
      }
      if (dp[i + 1][1][1] >= -n) {
        int y = p[i + 1], x = dp[i + 1][1][1];
        if (z < x) {
          if (y > dp[i][c][0]) {
            dp[i][c][0] = y, pre[i][c][0] = pair<bool, bool>(1, 1);
          }
        } else if (z < y) {
          if (x > dp[i][c][1]) {
            dp[i][c][1] = x, pre[i][c][1] = pair<bool, bool>(1, 1);
          }
        }
      }
    }
  }
  for (int i = 0; i < 2; ++i) {
    for (int j = 0; j < 2; ++j) {
      if (dp[1][i][j] >= -n) {
        cout << "YES\n";
        dfs(1, i, j);
        cout << '\n';
        return;
      }
    }
  }
  cout << "NO\n";
}
int main() {
  ios::sync_with_stdio(false);
  cin.tie(0);
  int T;
  cin >> T;
  while (T--) Solve();
  return 0;
}

```