Area

문제

A square field has been divided into $N^{2}N^2$ rectangular plots by drawing $(N-1)(N-1)$ vertical and $(N-1)(N-1)$ horizontal lines. The rows of plots are numbered $1\dots N1\; \backslash ldots\; N$ from bottom to top and the columns $1\dots N1\; \backslash ldots\; N$ from left to right, as shown on the figures below (the figures are not to scale).

[이미지 1]

The plots located at the intersection of the $ii$-th column and the $ii$-th row (for $1\le i\le N1\; \backslash le\; i\; \backslash le\; N$) are called the long diagonal. The plots located at the intersection of the $(i+1)(i+1)$-st column and the $ii$-th row (for $1\le i\le N-11\; \backslash le\; i\; \backslash le\; N-1$) are called the short diagonal.

You know the areas of the plots on the long and short diagonals. Calculate the area of the plot at the intersection of the $XX$-th column and the $YY$-th row.

입력

The first line contains the integer $NN$ ($2\le N\le 10002\; \backslash le\; N\; \backslash le\; 1\backslash ,000$).

The second line contains $NN$ integers $A_1,A_2,\dots ,A_{N}A\_1,\; A\_2,\; \backslash dots,\; A\_N$ ($1\le A_i\le {10}^{9}1\; \backslash le\; A\_i\; \backslash le\; 10^9$) --- the areas of the plots on the long diagonal.

The third line contains $N-1N-1$ integers $B_1,B_2,\dots ,B_{N-1}B\_1,\; B\_2,\; \backslash dots,\; B\_\{N-1\}$ ($1\le B_i\le {10}^{9}1\; \backslash le\; B\_i\; \backslash le\; 10^9$) --- the areas of the plots on the short diagonal.

The fourth line contains two integers $XX$ and $YY$ ($1\le X,Y\le N1\; \backslash le\; X,\; Y\; \backslash le\; N$) --- the coordinates of the plot whose area should be calculated.

출력

Output the area $SS$ of the plot located at the intersection of the $XX$-th column and the $YY$-th row. The answer should be represented as a sequence of lines, each containing two integers $P_{i}P\_i$ and $S_{i}S\_i$. The numbers $P_{i}P\_i$ must be distinct primes. The numbers $S_{i}S\_i$ must be non-zero integers such that $$S=P_1^{S_1}\cdot P_2^{S_2}\cdot P_3^{S_3}\cdot \dots \cdot P_k^{S_k},S\; =\; P\_1^\{S\_1\}\; \backslash cdot\; P\_2^\{S\_2\}\; \backslash cdot\; P\_3^\{S\_3\}\; \backslash cdot\; \backslash ldots\; \backslash cdot\; P\_k^\{S\_k\},$$ where $kk$ is the number of lines in the answer. The lines must be listed in increasing order of $P_{i}P\_i$. (Recall that an integer $PP$ is considered prime if it has exactly two positive integer divisors: $11$ and $PP$.)

If $S=1S\; =\; 1$, then output it as a single line "1 1".