You are given two arrays a and b, both of length n. All elements of both arrays are from 0 to n-1.

You can reorder elements of the array b (if you want, you may leave the order of elements as it is). After that, let array c be the array of length n, the i-th element of this array is c_i = (a_i + b_i) \% n, where x \% y is x modulo y.

Your task is to reorder elements of the array b to obtain the lexicographically minimum possible array c.

Array x of length n is lexicographically less than array y of length n, if there exists such i (1 ≤ i ≤ n), that x_i < y_i, and for any j (1 ≤ j < i) x_j = y_j.

Input

The first line of the input contains one integer n (1 ≤ n ≤ 2 ⋅ 10^5) — the number of elements in a, b and c.

The second line of the input contains n integers a_1, a_2, ..., a_n (0 ≤ a_i < n), where a_i is the i-th element of a.

The third line of the input contains n integers b_1, b_2, ..., b_n (0 ≤ b_i < n), where b_i is the i-th element of b.

Output

Print the lexicographically minimum possible array c. Recall that your task is to reorder elements of the array b and obtain the lexicographically minimum possible array c, where the i-th element of c is c_i = (a_i + b_i) \% n.

Examples

Input


4
0 1 2 1
3 2 1 1


Output


1 0 0 2 


Input


7
2 5 1 5 3 4 3
2 4 3 5 6 5 1


Output


0 0 0 1 0 2 4 
import sys
import bisect
input = sys.stdin.readline

n=int(input())
A=list(map(int,input().split()))
B=list(map(int,input().split()))

ALLB=[0]*(n)
LIST=[]

for b in B:
    ALLB[b]+=1
    LIST.append(b)

LIST=sorted(set(LIST))

R=[0]*(n)
L=[0]*(n)

for i in range(len(LIST)-1):
    R[LIST[i]]=LIST[i+1]

for i in range(1,len(LIST)):
    L[LIST[i]]=LIST[i-1]

R[LIST[len(LIST)-1]]=LIST[0]
L[LIST[0]]=LIST[-1]

ANS=[]

for a in A:
    #print(ALLB)
    #print(R,L)
    x=bisect.bisect_left(LIST,(-a)%n)
    if x==len(LIST):
        x=0

    #print(a,x,LIST[x])

    y=LIST[x]

    if ALLB[y]>0:
        ANS.append((a+y)%n)
        ALLB[y]-=1

        if ALLB[y]==0:

            L[R[y]],R[L[y]]=L[y],R[y]

    else:
        ZLIST=[]
        z=R[y]
        while ALLB[z]==0:
            ZLIST.append(z)
            z=R[z]

        for k in ZLIST:
            R[k]=z
            L[k]=L[z]

        ANS.append((a+z)%n)
        ALLB[z]-=1

        if ALLB[z]==0:

            L[R[z]],R[L[z]]=L[z],R[z]

print(*ANS)
