0106. Quantization Problem

Имя входного файла:	quant.in
Имя выходного файла:	quant.out
Ограничение по времени:	1 s
Ограничение по памяти:	32 megabytes

When entering some analog data into a computer, this information must be quantized. Quantization transforms each measured value x to some other value l(x) selected from the predefined set L of levels. Sometimes to reduce the influence of the levels set to the information, the group of levels sets L_i is used. The number of levels sets is usually chosen to be the power of 2.

When using the number of levels sets, some additional information should be used to specify which set was used for each quantization. However, providing this information may be too expensive – the better solution would be to choose more levels and use one set. To avoid the specification of the quantization set, the following technique is used. Suppose that n values x₁, x₂, …, x_n are to be quantized and the group of m=2^p levels sets {L_i}_i=0^m-1 each of size s=2^q is used to quantize it. After quantization x_j is replaced with some number l_j = ∈L_f(j). Instead of sending l_j, its ordinal number in L_f(j) is usually sent, let k_j be the ordinal number of l_j in L_f(j) (levels are numbered starting with 0). Take p least significant bits of k_j and say that the number k_j & (2^p-1) is the number of the levels set that will be used for next quantization, that is f(j+1) = k_j & (2^p-1).

Since the least significant bits of k_j are usually distributed quite randomly, the sets used for quantization change often and weakly depend on values of quantized data, thus this technique provides the good way to perform the quantization.

Usually to perform the quantization the closest to the value level of the levels set is chosen. However, using the technique described, sometimes it pays off to choose not the optimal level, but some other one, the ordinal number of which has other least significant bits, thus choosing another levels set for next measure and providing better approximation of quantized values in the future. Let us call the deviation of quantization the value Σ_j=1ⁿ|x_j - l_j |. Your task is given measures and levels sets to choose quantized value for each measure in such a way, that the deviation of quantization is minimal possible.

The first value is always quantized using set L₀.

Input file

The first line of the input file contains n (1 ≤ n ≤ 1000). The second line contains n integer numbers x_i ranging from 1 to 10⁶. The next line contains m and s (1 ≤ m ≤ 128, m ≤ s ≤ 128). Next m lines contain s integer numbers each – levels of the quantization sets given in increasing order for each set, all levels satisfy 1 ≤ level ≤ 10⁶.

Output file

First output the minimal possible deviation of the quantization. Then output n integer numbers in range from 0 to s - 1. For each input value output the number of the level in the corresponding levels set (k_j) used for this number to achieve the quantization required.

Examples:

quant.in	quant.out
3 8 8 19 2 4 5 10 15 20 3 7 13 17	5 1 1 3

Источник: Petrozavodsk Summer 2003. Andrew Stankevich Contest 1, Saturday, August 23
Автор: Andrew Stankevich

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