#include <bits/stdc++.h>
using namespace std;
template <typename T1, typename T2>
void chkmin(T1 &x, T2 y) {
  if (x > y) x = y;
}
template <typename T1, typename T2>
void chkmax(T1 &x, T2 y) {
  if (x < y) x = y;
}
namespace fastio {
char rbuf[1 << 23], *p1 = rbuf, *p2 = rbuf, wbuf[1 << 23], *p3 = wbuf;
inline char getc() {
  return p1 == p2 &&
                 (p2 = (p1 = rbuf) + fread(rbuf, 1, 1 << 23, stdin), p1 == p2)
             ? -1
             : *p1++;
}
inline void putc(char x) { (*p3++ = x); }
template <typename T>
void read(T &x) {
  x = 0;
  char c = getc();
  T neg = 0;
  while (!isdigit(c)) neg |= !(c ^ '-'), c = getc();
  while (isdigit(c)) x = (x << 3) + (x << 1) + (c ^ 48), c = getc();
  if (neg) x = (~x) + 1;
}
template <typename T>
void recursive_print(T x) {
  if (!x) return;
  recursive_print(x / 10);
  putc(x % 10 ^ 48);
}
template <typename T>
void print(T x) {
  if (!x) putc('0');
  if (x < 0) putc('-'), x = -x;
  recursive_print(x);
}
template <typename T>
void print(T x, char c) {
  print(x);
  putc(c);
}
void readstr(char *s) {
  char c = getc();
  while (c <= 32 || c >= 127) c = getc();
  while (c > 32 && c < 127) s[0] = c, s++, c = getc();
  (*s) = 0;
}
void printstr(string s) {
  for (int i = 0; i < s.size(); i++) putc(s[i]);
}
void printstr(char *s) {
  int len = strlen(s);
  for (int i = 0; i < len; i++) putc(s[i]);
}
void print_final() { fwrite(wbuf, 1, p3 - wbuf, stdout); }
}  // namespace fastio
const int MAXN = 1e6;
const int INF = 0x3f3f3f3f;
int n, p[MAXN + 5], dp[MAXN + 5][2], pre[MAXN + 5][2], res[MAXN + 5];
void upd(int x, int y, int p, int v) {
  if (dp[x][y] > v) dp[x][y] = v, pre[x][y] = p;
}
void dump(int x, int y) {
  if (!x) return;
  res[x] = (y) ? (-p[x]) : p[x];
  dump(x - 1, pre[x][y]);
}
void solve() {
  scanf("%d", &n);
  p[0] = n + 1;
  for (int i = 1; i <= n; i++) scanf("%d", &p[i]);
  for (int i = 0; i <= n; i++) dp[i][0] = dp[i][1] = INF;
  dp[0][1] = -p[0];
  for (int i = 0; i < n; i++)
    for (int j = 0; j < 2; j++)
      if (dp[i][j] < INF) {
        int v = (j) ? -p[i] : p[i];
        if (p[i + 1] > v) upd(i + 1, 0, j, dp[i][j]);
        if (p[i + 1] > dp[i][j]) upd(i + 1, 0, j, v);
        if (-p[i + 1] > v) upd(i + 1, 1, j, dp[i][j]);
        if (-p[i + 1] > dp[i][j]) upd(i + 1, 1, j, v);
      }
  if (dp[n][0] < INF)
    dump(n, 0);
  else if (dp[n][1] < INF)
    dump(n, 1);
  else
    return puts("NO"), void();
  puts("YES");
  for (int i = 1; i <= n; i++) printf("%d%c", res[i], " \n"[i == n]);
}
int main() {
  int qu;
  scanf("%d", &qu);
  while (qu--) solve();
  return 0;
}

### Prompt

Please provide a cpp coded solution to the problem described below:

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;
template <typename T1, typename T2>
void chkmin(T1 &x, T2 y) {
  if (x > y) x = y;
}
template <typename T1, typename T2>
void chkmax(T1 &x, T2 y) {
  if (x < y) x = y;
}
namespace fastio {
char rbuf[1 << 23], *p1 = rbuf, *p2 = rbuf, wbuf[1 << 23], *p3 = wbuf;
inline char getc() {
  return p1 == p2 &&
                 (p2 = (p1 = rbuf) + fread(rbuf, 1, 1 << 23, stdin), p1 == p2)
             ? -1
             : *p1++;
}
inline void putc(char x) { (*p3++ = x); }
template <typename T>
void read(T &x) {
  x = 0;
  char c = getc();
  T neg = 0;
  while (!isdigit(c)) neg |= !(c ^ '-'), c = getc();
  while (isdigit(c)) x = (x << 3) + (x << 1) + (c ^ 48), c = getc();
  if (neg) x = (~x) + 1;
}
template <typename T>
void recursive_print(T x) {
  if (!x) return;
  recursive_print(x / 10);
  putc(x % 10 ^ 48);
}
template <typename T>
void print(T x) {
  if (!x) putc('0');
  if (x < 0) putc('-'), x = -x;
  recursive_print(x);
}
template <typename T>
void print(T x, char c) {
  print(x);
  putc(c);
}
void readstr(char *s) {
  char c = getc();
  while (c <= 32 || c >= 127) c = getc();
  while (c > 32 && c < 127) s[0] = c, s++, c = getc();
  (*s) = 0;
}
void printstr(string s) {
  for (int i = 0; i < s.size(); i++) putc(s[i]);
}
void printstr(char *s) {
  int len = strlen(s);
  for (int i = 0; i < len; i++) putc(s[i]);
}
void print_final() { fwrite(wbuf, 1, p3 - wbuf, stdout); }
}  // namespace fastio
const int MAXN = 1e6;
const int INF = 0x3f3f3f3f;
int n, p[MAXN + 5], dp[MAXN + 5][2], pre[MAXN + 5][2], res[MAXN + 5];
void upd(int x, int y, int p, int v) {
  if (dp[x][y] > v) dp[x][y] = v, pre[x][y] = p;
}
void dump(int x, int y) {
  if (!x) return;
  res[x] = (y) ? (-p[x]) : p[x];
  dump(x - 1, pre[x][y]);
}
void solve() {
  scanf("%d", &n);
  p[0] = n + 1;
  for (int i = 1; i <= n; i++) scanf("%d", &p[i]);
  for (int i = 0; i <= n; i++) dp[i][0] = dp[i][1] = INF;
  dp[0][1] = -p[0];
  for (int i = 0; i < n; i++)
    for (int j = 0; j < 2; j++)
      if (dp[i][j] < INF) {
        int v = (j) ? -p[i] : p[i];
        if (p[i + 1] > v) upd(i + 1, 0, j, dp[i][j]);
        if (p[i + 1] > dp[i][j]) upd(i + 1, 0, j, v);
        if (-p[i + 1] > v) upd(i + 1, 1, j, dp[i][j]);
        if (-p[i + 1] > dp[i][j]) upd(i + 1, 1, j, v);
      }
  if (dp[n][0] < INF)
    dump(n, 0);
  else if (dp[n][1] < INF)
    dump(n, 1);
  else
    return puts("NO"), void();
  puts("YES");
  for (int i = 1; i <= n; i++) printf("%d%c", res[i], " \n"[i == n]);
}
int main() {
  int qu;
  scanf("%d", &qu);
  while (qu--) solve();
  return 0;
}

```