#include <bits/stdc++.h>
using namespace std;
inline int read() {
  int ans = 0, f = 1;
  char c = getchar();
  while (c > '9' || c < '0') {
    if (c == '-') f = -1;
    c = getchar();
  }
  while (c >= '0' && c <= '9') {
    ans = (ans << 1) + (ans << 3) + c - '0';
    c = getchar();
  }
  return ans * f;
}
inline void write(int x) {
  if (x < 0) putchar('-'), x = -x;
  if (x / 10) write(x / 10);
  putchar((char)(x % 10) + '0');
}
template <typename T>
inline T Abs(T a) {
  return a > 0 ? a : -a;
};
template <typename T, typename TT>
inline T Min(T a, TT b) {
  return a < b ? a : b;
}
template <typename T, typename TT>
inline T Max(T a, TT b) {
  return a < b ? b : a;
}
const int N = 1e6 + 5;
int t, n, a[N], dp[N][2][2], p1[N][2][2], p2[N][2][2], p3[N][2][2];
inline void update(int x, int y, int z, int v, int Y, int Z) {
  if (dp[x][y][z] > v) {
    dp[x][y][z] = v;
    p2[x][y][z] = Y;
    p3[x][y][z] = Z;
  }
}
void print(int x, int y, int z) {
  if (!x) return;
  int X, Y;
  if (y == 0) X = (z ? a[x] : -a[x]), Y = dp[x][y][z];
  if (y == 1) Y = (z ? a[x] : -a[x]), X = dp[x][y][z];
  print(x - 1, p2[x][y][z], p3[x][y][z]);
  if (Abs(X) == a[x]) write(X);
  if (Abs(Y) == a[x]) write(Y);
  putchar(' ');
}
signed main() {
  t = read();
  while (t--) {
    n = read();
    for (int i = 1; i <= n; ++i) a[i] = read();
    for (int i = 1; i <= n; ++i)
      for (int j = 0; j <= 1; ++j)
        for (int k = 0; k <= 1; ++k) dp[i][j][k] = 1e9;
    dp[1][0][0] = -1e9;
    dp[1][0][1] = -1e9;
    for (int i = 1; i <= n - 1; ++i)
      for (int j = 0; j <= 1; ++j)
        for (int k = 0; k <= 1; ++k)
          if (dp[i][j][k] != 1e9) {
            int x, y;
            if (j == 0) x = (k ? a[i] : -a[i]), y = dp[i][j][k];
            if (j == 1) y = (k ? a[i] : -a[i]), x = dp[i][j][k];
            if (a[i + 1] > y) {
              if (a[i + 1] > x)
                update(i + 1, 0, 1, y, j, k);
              else
                update(i + 1, 1, 1, x, j, k);
            }
            if (-a[i + 1] > y) {
              if (-a[i + 1] > x)
                update(i + 1, 0, 0, y, j, k);
              else
                update(i + 1, 1, 0, x, j, k);
            }
          }
    int flag = 1;
    for (int i = 0; i <= 1 && flag; ++i)
      for (int j = 0; j <= 1 && flag; ++j)
        if (dp[n][i][j] != 1e9) {
          puts("YES");
          print(n, i, j);
          puts("");
          flag = 0;
        }
    if (flag) puts("NO");
  }
  return 0;
}

### Prompt

Please formulate 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;
inline int read() {
  int ans = 0, f = 1;
  char c = getchar();
  while (c > '9' || c < '0') {
    if (c == '-') f = -1;
    c = getchar();
  }
  while (c >= '0' && c <= '9') {
    ans = (ans << 1) + (ans << 3) + c - '0';
    c = getchar();
  }
  return ans * f;
}
inline void write(int x) {
  if (x < 0) putchar('-'), x = -x;
  if (x / 10) write(x / 10);
  putchar((char)(x % 10) + '0');
}
template <typename T>
inline T Abs(T a) {
  return a > 0 ? a : -a;
};
template <typename T, typename TT>
inline T Min(T a, TT b) {
  return a < b ? a : b;
}
template <typename T, typename TT>
inline T Max(T a, TT b) {
  return a < b ? b : a;
}
const int N = 1e6 + 5;
int t, n, a[N], dp[N][2][2], p1[N][2][2], p2[N][2][2], p3[N][2][2];
inline void update(int x, int y, int z, int v, int Y, int Z) {
  if (dp[x][y][z] > v) {
    dp[x][y][z] = v;
    p2[x][y][z] = Y;
    p3[x][y][z] = Z;
  }
}
void print(int x, int y, int z) {
  if (!x) return;
  int X, Y;
  if (y == 0) X = (z ? a[x] : -a[x]), Y = dp[x][y][z];
  if (y == 1) Y = (z ? a[x] : -a[x]), X = dp[x][y][z];
  print(x - 1, p2[x][y][z], p3[x][y][z]);
  if (Abs(X) == a[x]) write(X);
  if (Abs(Y) == a[x]) write(Y);
  putchar(' ');
}
signed main() {
  t = read();
  while (t--) {
    n = read();
    for (int i = 1; i <= n; ++i) a[i] = read();
    for (int i = 1; i <= n; ++i)
      for (int j = 0; j <= 1; ++j)
        for (int k = 0; k <= 1; ++k) dp[i][j][k] = 1e9;
    dp[1][0][0] = -1e9;
    dp[1][0][1] = -1e9;
    for (int i = 1; i <= n - 1; ++i)
      for (int j = 0; j <= 1; ++j)
        for (int k = 0; k <= 1; ++k)
          if (dp[i][j][k] != 1e9) {
            int x, y;
            if (j == 0) x = (k ? a[i] : -a[i]), y = dp[i][j][k];
            if (j == 1) y = (k ? a[i] : -a[i]), x = dp[i][j][k];
            if (a[i + 1] > y) {
              if (a[i + 1] > x)
                update(i + 1, 0, 1, y, j, k);
              else
                update(i + 1, 1, 1, x, j, k);
            }
            if (-a[i + 1] > y) {
              if (-a[i + 1] > x)
                update(i + 1, 0, 0, y, j, k);
              else
                update(i + 1, 1, 0, x, j, k);
            }
          }
    int flag = 1;
    for (int i = 0; i <= 1 && flag; ++i)
      for (int j = 0; j <= 1 && flag; ++j)
        if (dp[n][i][j] != 1e9) {
          puts("YES");
          print(n, i, j);
          puts("");
          flag = 0;
        }
    if (flag) puts("NO");
  }
  return 0;
}

```