Nick had received an awesome array of integers a=[a_1, a_2, ..., a_n] as a gift for his 5 birthday from his mother. He was already going to explore its various properties but after unpacking he was disappointed a lot because the product a_1 ⋅ a_2 ⋅ ... a_n of its elements seemed to him not large enough.

He was ready to throw out the array, but his mother reassured him. She told him, that array would not be spoiled after the following operation: choose any index i (1 ≤ i ≤ n) and do a_i := -a_i - 1.

For example, he can change array [3, -1, -4, 1] to an array [-4, -1, 3, 1] after applying this operation to elements with indices i=1 and i=3. 

Kolya had immediately understood that sometimes it's possible to increase the product of integers of the array a lot. Now he has decided that he wants to get an array with the maximal possible product of integers using only this operation with its elements (possibly zero, one or more times, as many as he wants), it is not forbidden to do this operation several times for the same index. 

Help Kolya and print the array with the maximal possible product of elements a_1 ⋅ a_2 ⋅ ... a_n which can be received using only this operation in some order.

If there are multiple answers, print any of them.

Input

The first line contains integer n (1 ≤ n ≤ 10^{5}) — number of integers in the array.

The second line contains n integers a_1, a_2, …, a_n (-10^{6} ≤ a_i ≤ 10^{6}) — elements of the array

Output

Print n numbers — elements of the array with the maximal possible product of elements which can be received using only this operation in some order from the given array.

If there are multiple answers, print any of them.

Examples

Input


4
2 2 2 2


Output


-3 -3 -3 -3 

Input


1
0


Output


0 

Input


3
-3 -3 2


Output


-3 -3 2 
class cinn:
    def __init__(self):
        self.x=[]
    def cin(self,t=int):
        if(len(self.x)==0):
            a=input()
            self.x=a.split()
            self.x.reverse()
        return self.get(t)
    def get(self,t):
        return t(self.x.pop())
    def clist(self,n,t=int): #n is number of inputs, t is type to be casted
        l=[0]*n
        for i in range(n):
            l[i]=self.cin(t)
        return l
    def clist2(self,n,t1=int,t2=int,t3=int,tn=2):
        l=[0]*n
        for i in range(n):
            if(tn==2):
                a1=self.cin(t1)
                a2=self.cin(t2)
                l[i]=(a1,a2)
            elif (tn==3):
                a1=self.cin(t1)
                a2=self.cin(t2)
                a3=self.cin(t3)
                l[i]=(a1,a2,a3)
        return l
    def clist3(self,n,t1=int,t2=int,t3=int):
        return self.clist2(self,n,t1,t2,t3,3)
    def cout(self,i,ans=''):   
        if(ans==''):
            print("Case #"+str(i+1)+":", end=' ')
        else:
            print("Case #"+str(i+1)+":",ans)
    def printf(self,thing):
        print(thing,end='')
    def countlist(self,l,s=0,e=None):
        if(e==None):
            e=len(l)
        dic={}
        for el in range(s,e):
            if l[el] not in dic:
                dic[l[el]]=1
            else:
                dic[l[el]]+=1
        return dic
    def talk (self,x):
        print(x,flush=True)
    def dp1(self,k):
        L=[-1]*(k)
        return L
    def dp2(self,k,kk):
        L=[-1]*(k)
        for i in range(k):
            L[i]=[-1]*kk
        return L
    def isprime(self,n):
        if(n==1 or n==0):
            return False
        for i in range(2,int(n**0.5+1)):
            if(n%i==0):
                return False
        return True
    def factors(self,n):    
        from functools import reduce
        return set(reduce(list.__add__, 
                    ([i, n//i] for i in range(1, int(n**0.5) + 1) if n % i == 0)))
    def nthprime(self,n):
        #usable up to 10 thousand
        i=0
        s=2
        L=[]
        while(i<n):
            while(not self.isprime(s)):
                s+=1
            L.append(s)
            s+=1
            i+=1
        return L
    def matrixin(self,m,n,t=int):
        L=[]
        for i in range(m):
            p=self.clist(n,t)
            L.append(p)
        return L
    def seive(self,k):
        #1000000 tops
        n=k+1
        L=[True]*n
        L[1]=False
        L[0]=False
        for i in range(2,n):
            if(L[i]==True):
                for j in range(2*i,n,i):
                    L[j]=False
        return L
    def seiven(self,n,L):
        i=0
        for j in range(len(L)):
            if(L[j]==True):
                i+=1
            if(i==n):
                return j
    def matrixin2(self,m,t=int):
        L=[]
        for i in range(m):
            iny=self.cin(str)
            lsmall=[]
            for el in iny:
                lsmall.append(t(el))
            L.append(lsmall)
        return L
c=cinn()
n=c.cin()
L=c.clist(n)
minuses=0
for i in range(n):
    if(L[i]==0):
        L[i]=-1
    if(L[i]==-1):
        minuses+=1
left=n-minuses
if(left==0):
    if(n%2):
        L[0]=0
else:
    odd1=2*(minuses%2)-1
    oddleft=2*(left%2)-1
    dec=odd1*oddleft
    if dec==1:
        for i in range(len(L)):
            if(L[i]>0):
                L[i]=-L[i]-1
    else:
        for i in range(len(L)):
            if(L[i]>0):
                L[i]=-L[i]-1
        mini=0
        for el in L:
            if(el<mini and el!=-1):
                mini=el
        for i in range(len(L)):
            if(L[i]==mini):
                L[i]=-L[i]-1
                break
for el in L:
    print(el, end=" ")        
    
    
    