Give you N ( 1 <= N <= 200000 ) intervals, represented as [A, B], for example , interval s represented as [As,Bs].

For two intervals s and t, we say S covered by T if  At <= As and Bs <= Bt. Now my problem is easy, just tell me the question below: For each interval, how many intervals can cover it but not covered by it ?

Input

The input contains multiple test cases.
For each test case, the first line is an integer N ( 1 <= N <= 200000 ), which is the number of intervals. Then come N lines, the i-th of which contains two integers: A_i and Bi ( A_i , B_i will not exceed the 32-bit integer) specifying the two parameters described above.

Output

For each test case, output one line containing n space-separated integers, the i-th of which specifying the number of intervals that can cover it but not covered by it. 

Example

Input
3
0 1
-1 2
-2 3
 
2
0 1
0 1
Output:
2 1 0
0 0