There are n military men in the Berland army. Some of them have given orders to other military men by now. Given m pairs (xi, yi), meaning that the military man xi gave the i-th order to another military man yi.
It is time for reform! The Berland Ministry of Defence plans to introduce ranks in the Berland army. Each military man should be assigned a rank — integer number between 1 and k, inclusive. Some of them have been already assigned a rank, but the rest of them should get a rank soon.
Help the ministry to assign ranks to the rest of the army so that:
- for each of m orders it is true that the rank of a person giving the order (military man xi) is strictly greater than the rank of a person receiving the order (military man yi);
- for each rank from 1 to k there is at least one military man with this rank.
Output
Print n integers, where the i-th number is the rank of the i-th military man. If there are many solutions, print any of them.
If there is no solution, print the only number -1.
Примеры
| № | Входные данные | Выходные данные |
|
1
|
5 3 3
0 3 0 0 2
2 4
3 4
3 5
|
1 3 3 2 2
|
|
2
|
7 6 5
0 4 5 4 1 0 0
6 1
3 6
3 1
7 5
7 1
7 4
|
2 4 5 4 1 3 5
|
|
3
|
2 2 2
2 1
1 2
2 1
|
-1
|