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
  I=lambda:[*map(int,sys.stdin.readline().split())]
  N=1<<20
  P=print
  for _ in [0]*I()[0]:
  	n,=I();p=I();D=[[-N,-N,N,N]]
  	for i in range(1,n):
  		a,b,c,d=[N]*4;w,x,y,z=D[i-1];q,r=p[i],p[i-1]
  		if q>r:a=w
  		elif q>w:c=r
  		if -q>w:d=r
  		if x<a:a=x
  		if -q>-r:b=x
  		elif -q>x:d=-r
  		if q>y:a=min(a,r)
  		elif q>r:c=y
  		if q>z:a=min(a,-r)
  		else:c=min(c,z)
  		if -q>z:b=min(b,-r)
  		elif -q>-r:d=min(d,z)
  		D.append([a,b,c,d])
  	if D[-1]==[N]*4:P("NO")
  	else:
  		P("YES")
  		i,x,y=n,N-1,N-1
  		while i>0:
  			i-=1;a,b,c,d=D[i];v=p[i]
  			if a<=y and v<=x:x,y=v,a
  			elif b<=y and -v<=x:x,y=-v,b;p[i]=-v
  			elif c<=x and v<=y:x,y=c,v
  			elif d<=x and -v<=y:x,y=d,-v;p[i]=-v
  		P(' '.join(map(str,p)))