#include <bits/stdc++.h>
using namespace std;
const long long mod = 1000000007;
long long gcd(long long a, long long b) { return b == 0 ? a : gcd(b, a % b); }
const unsigned gen_seed =
    std::chrono::system_clock::now().time_since_epoch().count();
std::mt19937_64 gen(gen_seed);
int main() {
  int ta;
  scanf("%d", &ta);
  for (int ifa = 0; ifa < ta; ifa++) {
    int n;
    scanf("%d", &n);
    std::vector<int> a(n);
    for (int i = 0; i < n; i++) scanf("%d", &a[i]);
    for (int i = 0; i < n; i++) a[i] = abs(a[i]);
    const int INF = 2e9;
    std::vector<int> dm(n, INF);
    std::vector<int> dp(n, INF);
    std::vector<int> pp(n);
    std::vector<int> pm(n);
    dm[0] = -INF;
    dp[0] = -INF;
    pp[0] = 1;
    pm[0] = -1;
    for (int i = 0; i < n - 1; i++) {
      int to = a[i + 1];
      if (-to >= -a[i] && dm[i + 1] > dm[i]) {
        dm[i + 1] = dm[i];
        pm[i + 1] = -1;
      }
      if (-to >= dm[i] && dm[i + 1] > -a[i]) {
        dm[i + 1] = -a[i];
        pm[i + 1] = -1;
      }
      if (to >= -a[i] && dp[i + 1] > dm[i]) {
        dp[i + 1] = dm[i];
        pp[i + 1] = -1;
      }
      if (to >= dm[i] && dp[i + 1] > -a[i]) {
        dp[i + 1] = -a[i];
        pp[i + 1] = -1;
      }
      if (-to >= a[i] && dm[i + 1] > dp[i]) {
        dm[i + 1] = dp[i];
        pm[i + 1] = 1;
      }
      if (-to >= dp[i] && dm[i + 1] > a[i]) {
        dm[i + 1] = a[i];
        pm[i + 1] = 1;
      }
      if (to >= a[i] && dp[i + 1] > dp[i]) {
        dp[i + 1] = dp[i];
        pp[i + 1] = 1;
      }
      if (to >= dp[i] && dp[i + 1] > a[i]) {
        dp[i + 1] = a[i];
        pp[i + 1] = 1;
      }
    }
    int cur = n - 1;
    int sg = 0;
    if (dp[n - 1] != INF) sg = 1;
    if (dm[n - 1] != INF) sg = -1;
    if (sg == 0)
      printf("NO\n");
    else {
      while (cur >= 0) {
        a[cur] *= sg;
        if (sg > 0)
          sg = pp[cur--];
        else
          sg = pm[cur--];
      }
      printf("YES\n");
      for (int i = 0; i < n; i++) printf("%d ", a[i]);
      printf("\n");
    }
  }
}

### Prompt

Your challenge is to write a Cpp solution 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;
const long long mod = 1000000007;
long long gcd(long long a, long long b) { return b == 0 ? a : gcd(b, a % b); }
const unsigned gen_seed =
    std::chrono::system_clock::now().time_since_epoch().count();
std::mt19937_64 gen(gen_seed);
int main() {
  int ta;
  scanf("%d", &ta);
  for (int ifa = 0; ifa < ta; ifa++) {
    int n;
    scanf("%d", &n);
    std::vector<int> a(n);
    for (int i = 0; i < n; i++) scanf("%d", &a[i]);
    for (int i = 0; i < n; i++) a[i] = abs(a[i]);
    const int INF = 2e9;
    std::vector<int> dm(n, INF);
    std::vector<int> dp(n, INF);
    std::vector<int> pp(n);
    std::vector<int> pm(n);
    dm[0] = -INF;
    dp[0] = -INF;
    pp[0] = 1;
    pm[0] = -1;
    for (int i = 0; i < n - 1; i++) {
      int to = a[i + 1];
      if (-to >= -a[i] && dm[i + 1] > dm[i]) {
        dm[i + 1] = dm[i];
        pm[i + 1] = -1;
      }
      if (-to >= dm[i] && dm[i + 1] > -a[i]) {
        dm[i + 1] = -a[i];
        pm[i + 1] = -1;
      }
      if (to >= -a[i] && dp[i + 1] > dm[i]) {
        dp[i + 1] = dm[i];
        pp[i + 1] = -1;
      }
      if (to >= dm[i] && dp[i + 1] > -a[i]) {
        dp[i + 1] = -a[i];
        pp[i + 1] = -1;
      }
      if (-to >= a[i] && dm[i + 1] > dp[i]) {
        dm[i + 1] = dp[i];
        pm[i + 1] = 1;
      }
      if (-to >= dp[i] && dm[i + 1] > a[i]) {
        dm[i + 1] = a[i];
        pm[i + 1] = 1;
      }
      if (to >= a[i] && dp[i + 1] > dp[i]) {
        dp[i + 1] = dp[i];
        pp[i + 1] = 1;
      }
      if (to >= dp[i] && dp[i + 1] > a[i]) {
        dp[i + 1] = a[i];
        pp[i + 1] = 1;
      }
    }
    int cur = n - 1;
    int sg = 0;
    if (dp[n - 1] != INF) sg = 1;
    if (dm[n - 1] != INF) sg = -1;
    if (sg == 0)
      printf("NO\n");
    else {
      while (cur >= 0) {
        a[cur] *= sg;
        if (sg > 0)
          sg = pp[cur--];
        else
          sg = pm[cur--];
      }
      printf("YES\n");
      for (int i = 0; i < n; i++) printf("%d ", a[i]);
      printf("\n");
    }
  }
}

```