Problem Statement

There is a non-negative integer $X$ initially equal to $S$. One can perform the following operations, in any order, any number of times:

• Add $1$ to $X$. This has a cost of $A$.
• Choose $i$ between $1$ and $N$, and replace $X$ with $X \\oplus Y_i$. This has a cost of $C_i$. Here, $\\oplus$ denotes bitwise $\\mathrm{XOR}$.

Find the smallest total cost to make $X$ equal to a given non-negative integer $T$, or report that this is impossible.

What is bitwise $\\mathrm{XOR}$?

The bitwise $\\mathrm{XOR}$ of non-negative integers $A$ and $B$, $A \\oplus B$, is defined as follows:

• When $A \\oplus B$ is written in base two, the digit in the $2^k$'s place ($k \\geq 0$) is $1$ if exactly one of the digits in that place of $A$ and $B$ is $1$, and $0$ otherwise.

For example, we have $3 \\oplus 5 = 6$ (in base two: $011 \\oplus 101 = 110$).
Generally, the bitwise $\\mathrm{XOR}$ of $k$ non-negative integers $p_1, p_2, p_3, \\dots, p_k$ is defined as $(\\dots ((p_1 \\oplus p_2) \\oplus p_3) \\oplus \\dots \\oplus p_k)$. We can prove that this value does not depend on the order of $p_1, p_2, p_3, \\dots, p_k$.

Constraints

• $1 \\leq N \\leq 8$
• $0 \\leq S, T < 2^{40}$
• $0 \\leq A \\leq 10^5$
• $0 \\leq Y_i < 2^{40}$ ($1 \\leq i \\leq N$)
• $0 \\leq C_i \\leq 10^{16}$ ($1 \\leq i \\leq N$)
• All values in the input are integers.

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Input

Input is given from Standard Input in the following format:

$N$ $S$ $T$ $A$ $Y_1$ $C_1$ $\\vdots$ $Y_N$ $C_N$

Output

If the task is impossible, print -1. Otherwise, print the smallest total cost.

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Sample Input 1

1 15 0 1
8 2

Sample Output 1

5

You can make $X$ equal to $T$ in the following manner:

• Choose $i=1$ and replace $X$ with $X \\oplus 8$ to get $X=7$. This has a cost of $2$.
• Add $1$ to $X$ to get $X=8$. This has a cost of $1$.
• Choose $i=1$ and replace $X$ with $X \\oplus 8$ to get $X=0$. This has a cost of $2$.

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Sample Input 2

3 21 10 100
30 1
12 1
13 1

Sample Output 2

3

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Sample Input 3

1 2 0 1
1 1

Sample Output 3

-1

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Sample Input 4

8 352217 670575 84912
239445 2866
537211 16
21812 6904
50574 8842
380870 5047
475646 8924
188204 2273
429397 4854

Sample Output 4

563645