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NSU-construction site

Above the arena of the huge sports complex of the independent LavnyThe niversity (NSU) decided to build an overlap. The overlap will be built using adhesive technology and consist of blocks glued together. The block is a light rectangular parallelepiped. Two blocks can be glued together if they touch overlapping parts of the side faces of a non-zero area.

NSU presented a plan of the complex, which has the form of a rectangle of size W by L. In this case, one of the corners of the rectangle is at the beginning of the coordinate system, and the other has coordinates (W, L). The walls of the complex are parallel to the coordinate axes.

The contractors informed the NSU that they are ready to manufacture the blocks and install them by a certain date. For each block, the place of its possible installation is fixed, which coincides in size with this block. The locations are chosen so that the edges of the blocks are parallel to the coordinate axes. The installation locations of the blocks do not overlap.


According to the technical conditions, the overlap should consist of such a set of glued blocks that contains a solid horizontal layer of non-zero thickness. In a hurry to put the complex into operation, NSU decided to build an overlap from the minimum possible number of blocks.

It is required to write a program that allows you to select the minimum number of blocks that, being installed at the places specified by contractors, form an overlap, or determine that this cannot be done. The height at which the overlap is formed does not matter.

Input data

The first line of the input file contains three integers: N is the number of possible blocks (1 ≤ N ≤ 10 5) and the sizes of the complex W and L (1 ≤ W, L ≤ 10 4). Each of the following N lines describes the installation location of one block, determined by the coordinates of opposite angles: (x 1, y 1, z 1) and (x 2, y 2, z 2), with 0 ≤ x 1 < x 2 ≤ W, 0 ≤ y 1 < y 2 ≤ L, 0 ≤ z 1 < z 2 ≤ 10 9. All numbers in the input file are integers and separated by spaces or line breaks.

It is guaranteed that the installation locations of the blocks do not intersect with each other.

Output data

The first line of the output file must contain either the word "YES", if an overlap can be built, otherwise the word "NO". In the first case, the second line of the output file should contain the minimum number of blocks forming an overlap, and the subsequent lines should contain the numbers of these blocks, in accordance with the order in which they are listed in the input file.

If several minimal sets of blocks are possible, output any of them.

Notes

Solutions that work correctly when all the numbers in the input file do not exceed 100 will be evaluated out of 40 points.

Examples
Input data
1 10 10
0 0 0 10 10 10
Output data
YES
1
1
Input data
2 10 10
0 0 0 10 5 5
0 5 5 10 10 10
Output data
NO

This problem on informatics

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