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
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

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

#include <bits/stdc++.h>
using namespace std;
class config {
 public:
  int hi;
  int lo;
  int last_value;
  config* last_node;
  bool operator<=(config& c) {
    if (hi != c.hi) return hi < c.hi;
    if (lo != c.lo) return (lo < c.lo);
    return true;
  }
};
bool comp(config* c1, config* c2) {
  if (c1->hi != c2->hi) return c1->hi < c2->hi;
  if (c1->lo != c2->lo) return (c1->lo < c2->lo);
  return true;
}
int p[1000001];
int ans[1000001];
int main() {
  int t, n;
  cin >> t;
  while (t--) {
    cin >> n;
    for (int i = 0; i < n; i++) {
      cin >> p[i];
    }
    vector<config*> configs;
    configs.push_back(new config{-1000001, -1000002, 0, 0});
    for (int k = 0; k < n; k++) {
      int i = p[k];
      vector<config*> next;
      for (auto c : configs) {
        if (i > c->hi)
          next.push_back(new config{i, c->lo, i, c});
        else if (i > c->lo)
          next.push_back(new config{c->hi, i, i, c});
        if (-i > c->hi)
          next.push_back(new config{-i, c->lo, -i, c});
        else if (-i > c->lo)
          next.push_back(new config{c->hi, -i, -i, c});
      }
      sort(next.begin(), next.end(), comp);
      configs.clear();
      for (config* c : next) {
        if (configs.size() == 0 || configs.back()->hi == c->hi)
          configs.push_back(c);
      }
    }
    if (configs.size()) {
      cout << "YES" << endl;
      config c = *configs.back();
      for (int i = n - 1; i >= 0; i--) {
        ans[i] = c.last_value;
        c = *c.last_node;
      }
      for (int i = 0; i < n; i++) {
        cout << ans[i] << " ";
      }
      cout << endl;
    } else {
      cout << "NO" << endl;
    }
  }
}
