#include <bits/stdc++.h>
using namespace std;
mt19937 rnd(chrono::steady_clock::now().time_since_epoch().count());
mt19937 rnf(2106);
const int N = 1000006, INF = 1000000009;
int n;
int a[N];
int dp[N][2];
int p[N][2];
void minh(int& x, int& px, int y, int u) {
  if (y < x) {
    x = y;
    px = u;
  }
}
bool solv() {
  dp[1][0] = dp[1][1] = -INF;
  for (int i = 2; i <= n; ++i) dp[i][0] = dp[i][1] = INF;
  for (int i = 1; i < n; ++i) {
    if (a[i] < a[i + 1]) {
      minh(dp[i + 1][0], p[i + 1][0], dp[i][0], 0);
    }
    if (dp[i][0] < a[i + 1]) {
      minh(dp[i + 1][0], p[i + 1][0], a[i], 0);
    }
    if (dp[i][0] < -a[i + 1]) {
      minh(dp[i + 1][1], p[i + 1][1], a[i], 0);
    }
    if (-a[i] < a[i + 1]) {
      minh(dp[i + 1][0], p[i + 1][0], dp[i][1], 1);
    }
    if (-a[i] < -a[i + 1]) {
      minh(dp[i + 1][1], p[i + 1][1], dp[i][1], 1);
    }
    if (dp[i][1] < a[i + 1]) {
      minh(dp[i + 1][0], p[i + 1][0], -a[i], 1);
    }
    if (dp[i][1] < -a[i + 1]) {
      minh(dp[i + 1][1], p[i + 1][1], -a[i], 1);
    }
  }
  if (dp[n][0] != INF || dp[n][1] != INF) {
    int u;
    if (dp[n][0] != INF)
      u = 0;
    else
      u = 1;
    for (int i = n; i >= 1; --i) {
      if (u == 1) a[i] *= -1;
      u = p[i][u];
    }
    cout << "YES\n";
    for (int i = 1; i <= n; ++i) cout << a[i] << ' ';
    cout << "\n";
    return true;
  }
  cout << "NO\n";
  return false;
}
bool solv0() {
  for (int x = 0; x < (1 << n); ++x) {
    for (int i = 1; i <= n; ++i) {
      if ((x & (1 << (i - 1)))) a[i] *= -1;
    }
    bool z = true;
    for (int i = 1; i <= n; ++i) {
      for (int j = i + 1; j <= n; ++j) {
        for (int k = j + 1; k <= n; ++k) {
          if (a[i] > a[j] && a[j] > a[k]) {
            z = false;
            break;
          }
        }
        if (!z) break;
      }
      if (!z) break;
    }
    if (z) {
      return true;
      for (int i = 1; i <= n; ++i) {
        if ((x & (1 << (i - 1)))) a[i] *= -1;
      }
      return true;
    }
    for (int i = 1; i <= n; ++i) {
      if ((x & (1 << (i - 1)))) a[i] *= -1;
    }
  }
  return false;
}
int main() {
  ios_base::sync_with_stdio(false), cin.tie(0);
  int tt = 100;
  cin >> tt;
  while (tt--) {
    cin >> n;
    for (int i = 1; i <= n; ++i) cin >> a[i];
    solv();
  }
  return 0;
}

### Prompt

Please create a solution in cpp to 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;
mt19937 rnd(chrono::steady_clock::now().time_since_epoch().count());
mt19937 rnf(2106);
const int N = 1000006, INF = 1000000009;
int n;
int a[N];
int dp[N][2];
int p[N][2];
void minh(int& x, int& px, int y, int u) {
  if (y < x) {
    x = y;
    px = u;
  }
}
bool solv() {
  dp[1][0] = dp[1][1] = -INF;
  for (int i = 2; i <= n; ++i) dp[i][0] = dp[i][1] = INF;
  for (int i = 1; i < n; ++i) {
    if (a[i] < a[i + 1]) {
      minh(dp[i + 1][0], p[i + 1][0], dp[i][0], 0);
    }
    if (dp[i][0] < a[i + 1]) {
      minh(dp[i + 1][0], p[i + 1][0], a[i], 0);
    }
    if (dp[i][0] < -a[i + 1]) {
      minh(dp[i + 1][1], p[i + 1][1], a[i], 0);
    }
    if (-a[i] < a[i + 1]) {
      minh(dp[i + 1][0], p[i + 1][0], dp[i][1], 1);
    }
    if (-a[i] < -a[i + 1]) {
      minh(dp[i + 1][1], p[i + 1][1], dp[i][1], 1);
    }
    if (dp[i][1] < a[i + 1]) {
      minh(dp[i + 1][0], p[i + 1][0], -a[i], 1);
    }
    if (dp[i][1] < -a[i + 1]) {
      minh(dp[i + 1][1], p[i + 1][1], -a[i], 1);
    }
  }
  if (dp[n][0] != INF || dp[n][1] != INF) {
    int u;
    if (dp[n][0] != INF)
      u = 0;
    else
      u = 1;
    for (int i = n; i >= 1; --i) {
      if (u == 1) a[i] *= -1;
      u = p[i][u];
    }
    cout << "YES\n";
    for (int i = 1; i <= n; ++i) cout << a[i] << ' ';
    cout << "\n";
    return true;
  }
  cout << "NO\n";
  return false;
}
bool solv0() {
  for (int x = 0; x < (1 << n); ++x) {
    for (int i = 1; i <= n; ++i) {
      if ((x & (1 << (i - 1)))) a[i] *= -1;
    }
    bool z = true;
    for (int i = 1; i <= n; ++i) {
      for (int j = i + 1; j <= n; ++j) {
        for (int k = j + 1; k <= n; ++k) {
          if (a[i] > a[j] && a[j] > a[k]) {
            z = false;
            break;
          }
        }
        if (!z) break;
      }
      if (!z) break;
    }
    if (z) {
      return true;
      for (int i = 1; i <= n; ++i) {
        if ((x & (1 << (i - 1)))) a[i] *= -1;
      }
      return true;
    }
    for (int i = 1; i <= n; ++i) {
      if ((x & (1 << (i - 1)))) a[i] *= -1;
    }
  }
  return false;
}
int main() {
  ios_base::sync_with_stdio(false), cin.tie(0);
  int tt = 100;
  cin >> tt;
  while (tt--) {
    cin >> n;
    for (int i = 1; i <= n; ++i) cin >> a[i];
    solv();
  }
  return 0;
}

```