Three Little Pigs
Recall that after defeating the wolf, all three little pigs settled at Naf-Naf's house. During the long winter evenings in their cozy stone home, they would read books and play games. However, as winter dragged on, even their favorite games became tiresome. So, the pigs decided to create a new board game, similar to checkers or chess, but designed for three players. They drew a triangular board and placed an equal number of points at equal intervals along the sides of the triangle. Then, they connected these points on adjacent sides with segments parallel to the third side. This resulted in a triangular grid made up of smaller triangular cells (a small section of which is shown in the picture).
The pigs realized that they often argued during games, so they decided that moves in their new game should be recorded. To do this, they needed to number the triangles and their vertices. They numbered the vertices, choosing one as the starting point (as shown in rectangular frames in the picture), and numbered the triangles (as shown in circles in the picture).
Clever Naf-Naf noticed that the vertex numbers of the triangular grid could be easily determined by the triangle's number. Therefore, when recording moves, there was no need to write down the vertex numbers. For example, triangle 7 has vertices 5, 8, and 9, while triangle 11 has vertices 7, 8, and 12, and so on. However, Nif-Nif and Nuf-Nuf didn't immediately grasp this concept, so they needed a program to calculate the vertex numbers of a triangle based on its number.
Input
The first line contains a single integer – the number of the triangle N (1 ≤ N ≤ 10^9).
Assume that the pigs have created a sufficiently large board so that such a triangle exists.
Output
Output a single line with three integers separated by spaces – the vertex numbers of the specified triangle in ascending order.