You are given n vectors of $\mathbb{Z}_2^m$. So, that's just arrays of zeroes and ones of length m.

Let's define addition of multiple vectors as a vector whose i-th coordinate is equal to XOR of i-th coordinates of the vectors that is being added.

Find non-empty subset of the n given vectors such that their addition is a vector containing few number of ones.

Scoring:
Let u be the result vector of addition of the selected subset.

Define $\mathrm{pop}(v)$ as number of ones in v.

Score for one testcase defined as $\mathrm{score}= 10^5 \cdot \frac{\max(0, k - \mathrm{pop}(u))}{k},$ where $k = m - n + 1$.

Goal is to maximize score, which corresponds to minimizing $\mathrm{pop}(v)$.

Input Format:

first line contains two integers n and m.

each of the next n lines describes a vector as a string containing m characters of either 0 or 1

$n \; m$
$v_{11} \dots v_{1m}$
$\dots$
$v_{n1} \dots v_{nm}$

Output Format:
In first line, output number of vectors you take. On next line, output vector numbers in any order.

S
$s_1 \dots s_{|S|}$

Testcase Generation
Each of values $v_{ij}$ will be chosen randomly and equiprobable from $\{0, 1\}$.

after the contest, all tests will be replaces with equivalent tests but with different seed then all solutions will be rejudged.

Test Groups
Test organized in 4 groups. Each group consist of 25 testcases.
Group #1
$n = 30, m = 100$.

Group #2
$n = 50, m = 100$.

Group #3
$n = 70, m = 100$.

Group #4
$n = 90, m = 100$.