description: 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
solution: import sys
  inpu=sys.stdin.readline
  prin=sys.stdout.write
  I=lambda:[*map(int,inpu().split())]
  big = 1 << 20
  t, = I()
  for _ in range(t):
  	n, = I()
  	p = I()
  
  	dp = [[-big, -big, big, big]]
  	# 0 -> x,+
  	# 1 -> x,-
  	# 2 -> y,+
  	# 3 -> y,-
  	for i in range(1, n):
  		a, b, c, d = big, big, big, big
  		y = dp[i - 1][0]
  		if p[i] > p[i - 1]:
  			a = y
  		elif p[i] > y:
  			c = p[i - 1]
  		if -p[i] > y:
  			d = p[i - 1]
  		y = dp[i - 1][1]
  		if y < a:
  			a = y
  		if -p[i] > -p[i - 1]:
  			b = y
  		elif -p[i] > y:
  			d = -p[i - 1]
  		x = dp[i - 1][2]
  		if p[i] > x:
  			a = min(a, p[i - 1])
  		elif p[i] > p[i - 1]:
  			c = x
  		x = dp[i - 1][3]
  		if p[i] > x:
  			a = min(a, -p[i - 1])
  		else:
  			c = min(c, x)
  		if -p[i] > x:
  			b = min(b, -p[i - 1])
  		elif -p[i] > -p[i - 1]:
  			d = min(d, x)
  		dp.append([a, b, c, d])
  	if dp[-1] == [big, big, big, big]:
  		print("NO")
  	else:
  		print("YES")
  		i = n - 1
  		x = big - 1
  		y = big - 1
  		while i >= 0:
  			a, b, c, d = dp[i]
  			val = p[i]
  			if a <= y and val <= x:
  				x, y = val, a
  			elif b <= y and -val <= x:
  				x, y = -val, b
  				p[i] = -val
  			elif c <= x and val <= y:
  				x, y = c, val
  			elif d <= x and -val <= y:
  				x, y = d, -val
  				p[i] = -val
  			i -= 1
  		print(' '.join(str(guy) for guy in p))
  