Triangular Room

Many books on entertaining mathematics contain following task. Arrange 3 chairs around the perimeter of triangular room such that there would be 2 chairs near each wall. The solution of this problem is to put one chair in each corner of the room.

Consider more general problem. Let the room is represented by triangle ABC. The total number of chairs n, the number of chairs n_AB , which must be standing near wall AB, the number of chairs n_BC, which must be standing near wall BC, and the number of chairs n_AC, which must be standing near wall AC are given. It is necessary to find the number of arrangements satisfying conditions. Chairs can be put in corners of the room or along walls only, and should not be put in the center of the room. In each corner you can put any number of chairs.

Input

The input file contains integer numbers n, n_AB, n_BC, n_AC (0 ≤ n, n_AB, n_BC, n_AC ≤ 10^18).

Output

Write the number of different chairs arrangements in first line of the input file. If there is at least one arrangement, write 6 nonnegative integer numbers in the second line: k_A, k_AB, k_B, k_BC, k_C, k_AC, represented number of chairs, which must be put in the corner A, along the wall AB, in the corner B, along the wall BC, in the corner C and along the wall AC respectively.

Examples