#include <bits/stdc++.h>
using namespace std;
bool home = false;
const int N = (int)1e6 + 7;
const int INF = (int)1e9;
int n;
int a[N][2];
int dp[N][2][2];
vector<int> par[N][2][2];
int main() {
  if (!home) {
    ios::sync_with_stdio(0);
    cin.tie(0);
  }
  int tests;
  cin >> tests;
  while (tests--) {
    cin >> n;
    for (int i = 0; i <= n + 1; i++) {
      dp[i][0][0] = dp[i][0][1] = dp[i][1][0] = dp[i][1][1] = INF;
      par[i][0][0] = par[i][0][1] = par[i][1][0] = par[i][1][1] = {-1, -1, -1};
    }
    for (int i = 1; i <= n; i++) {
      cin >> a[i][0];
      a[i][1] = -a[i][0];
    }
    function<void(int, int, int, int, int, int)> upd = [&](int i, int m1,
                                                           int m2, int c1,
                                                           int c2, int cur) {
      assert(m1 == a[i][0] || m1 == a[i][1] || m2 == a[i][0] || m2 == a[i][1]);
      if (m1 == a[i][0] || m1 == a[i][1]) {
        if (m2 < dp[i][0][(m1 == a[i][1])]) {
          dp[i][0][(m1 == a[i][1])] = m2;
          par[i][0][(m1 == a[i][1])] = {c1, c2, cur};
        }
      } else {
        if (m1 < dp[i][1][(m2 == a[i][1])]) {
          dp[i][1][(m2 == a[i][1])] = m1;
          par[i][1][(m2 == a[i][1])] = {c1, c2, cur};
        }
      }
    };
    upd(1, a[1][1], -INF, 0, 0, 0);
    for (int i = 1; i < n; i++) {
      for (int pos = 0; pos <= 1; pos++) {
        for (int who = 0; who <= 1; who++) {
          int m1 = a[i][who], m2 = dp[i][pos][who];
          if (pos) {
            swap(m1, m2);
          }
          for (int t = 0; t <= 1; t++) {
            int x = a[i + 1][t];
            if (x > m1) {
              upd(i + 1, x, m2, pos, who, x);
            } else {
              if (x > m2) {
                upd(i + 1, m1, x, pos, who, x);
              }
            }
          }
        }
      }
    }
    bool good = false;
    int p, w;
    for (int pos = 0; pos <= 1; pos++) {
      for (int who = 0; who <= 1; who++) {
        if (dp[n][pos][who] != INF) {
          good = true;
          p = pos;
          w = who;
        }
      }
    }
    if (!good) {
      cout << "NO\n";
      continue;
    }
    vector<int> sol;
    for (int i = n; i >= 2; i--) {
      sol.push_back(par[i][p][w][2]);
      int p2, w2;
      p2 = par[i][p][w][0];
      w2 = par[i][p][w][1];
      assert(p2 != -1);
      assert(w2 != -1);
      p = p2;
      w = w2;
    }
    sol.push_back(a[1][1]);
    cout << "YES\n";
    reverse(sol.begin(), sol.end());
    for (auto &x : sol) {
      cout << x << " ";
    }
    cout << "\n";
  }
  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;
bool home = false;
const int N = (int)1e6 + 7;
const int INF = (int)1e9;
int n;
int a[N][2];
int dp[N][2][2];
vector<int> par[N][2][2];
int main() {
  if (!home) {
    ios::sync_with_stdio(0);
    cin.tie(0);
  }
  int tests;
  cin >> tests;
  while (tests--) {
    cin >> n;
    for (int i = 0; i <= n + 1; i++) {
      dp[i][0][0] = dp[i][0][1] = dp[i][1][0] = dp[i][1][1] = INF;
      par[i][0][0] = par[i][0][1] = par[i][1][0] = par[i][1][1] = {-1, -1, -1};
    }
    for (int i = 1; i <= n; i++) {
      cin >> a[i][0];
      a[i][1] = -a[i][0];
    }
    function<void(int, int, int, int, int, int)> upd = [&](int i, int m1,
                                                           int m2, int c1,
                                                           int c2, int cur) {
      assert(m1 == a[i][0] || m1 == a[i][1] || m2 == a[i][0] || m2 == a[i][1]);
      if (m1 == a[i][0] || m1 == a[i][1]) {
        if (m2 < dp[i][0][(m1 == a[i][1])]) {
          dp[i][0][(m1 == a[i][1])] = m2;
          par[i][0][(m1 == a[i][1])] = {c1, c2, cur};
        }
      } else {
        if (m1 < dp[i][1][(m2 == a[i][1])]) {
          dp[i][1][(m2 == a[i][1])] = m1;
          par[i][1][(m2 == a[i][1])] = {c1, c2, cur};
        }
      }
    };
    upd(1, a[1][1], -INF, 0, 0, 0);
    for (int i = 1; i < n; i++) {
      for (int pos = 0; pos <= 1; pos++) {
        for (int who = 0; who <= 1; who++) {
          int m1 = a[i][who], m2 = dp[i][pos][who];
          if (pos) {
            swap(m1, m2);
          }
          for (int t = 0; t <= 1; t++) {
            int x = a[i + 1][t];
            if (x > m1) {
              upd(i + 1, x, m2, pos, who, x);
            } else {
              if (x > m2) {
                upd(i + 1, m1, x, pos, who, x);
              }
            }
          }
        }
      }
    }
    bool good = false;
    int p, w;
    for (int pos = 0; pos <= 1; pos++) {
      for (int who = 0; who <= 1; who++) {
        if (dp[n][pos][who] != INF) {
          good = true;
          p = pos;
          w = who;
        }
      }
    }
    if (!good) {
      cout << "NO\n";
      continue;
    }
    vector<int> sol;
    for (int i = n; i >= 2; i--) {
      sol.push_back(par[i][p][w][2]);
      int p2, w2;
      p2 = par[i][p][w][0];
      w2 = par[i][p][w][1];
      assert(p2 != -1);
      assert(w2 != -1);
      p = p2;
      w = w2;
    }
    sol.push_back(a[1][1]);
    cout << "YES\n";
    reverse(sol.begin(), sol.end());
    for (auto &x : sol) {
      cout << x << " ";
    }
    cout << "\n";
  }
  return 0;
}

```