```go
package main

import (
	"bufio"
	"fmt"
	"os"
	"sort"
)

func main() {
	in := bufio.NewReader(os.Stdin)
	var n int
	fmt.Fscan(in, &n)
	L := get(n)
	fmt.Println(len(L))
	for _, part := range L {
		for ip, pile := range part {
			if ip > 0 {
				fmt.Print(" | ")
			}
			for it, toy := range pile {
				if it > 0 {
					fmt.Print(" ")
				}
				fmt.Print(toy)
			}
		}
		fmt.Println()
	}
}

func copyBlocks(b [][]int) [][]int {
	res := make([][]int, len(b))
	for i := range res {
		res[i] = make([]int, len(b[i]))
		copy(res[i], b[i])
	}
	return res
}

func get(n int) [][][]int {
	if n == 1 {
		return [][][]int{{{1}}}
	}
	prev := get(n - 1)
	var result [][][]int
	for idx, p := range prev {
		blocks := copyBlocks(p)
		k := len(blocks)
		var sub [][][]int
		if idx%2 == 0 {
			for j := 0; j < k; j++ {
				np := copyBlocks(blocks)
				np[j] = append(np[j], n)
				sort.Ints(np[j])
				sort.Slice(np, func(a, b int) bool {
					return np[a][0] < np[b][0]
				})
				sub = append(sub, np)
			}
			np := copyBlocks(blocks)
			np = append(np, []int{n})
			sort.Slice(np, func(a, b int) bool {
				return np[a][0] < np[b][0]
			})
			sub = append(sub, np)
		} else {
			np := copyBlocks(blocks)
			np = append(np, []int{n})
			sort.Slice(np, func(a, b int) bool {
				return np[a][0] < np[b][0]
			})
			sub = append(sub, np)
			for j := k - 1; j >= 0; j-- {
				np := copyBlocks(blocks)
				np[j] = append(np[j], n)
				sort.Ints(np[j])
				sort.Slice(np, func(a, b int) bool {
					return np[a][0] < np[b][0]
				})
				sub = append(sub, np)
			}
		}
		result = append(result, sub...)
	}
	return result
}
```