Given the following C code and unoptimized assembly code, your task is to generate highly optimized x86-64 assembly code.
C Code:

```c
#include <stdio.h>

int main(void) {

  int n;
  scanf("%d", &n);
  int a[n+1];
  for (int i = 1; i <= n; i++) {
    scanf("%d", &a[i]);
  }
  int put[n+1];
  int ball;
  int ball_sum = 0;
  for (int i = n; i > 0; i--) {
    ball = 0;
    for (int j = 2; i*j <= n; j++) {
      ball += put[i*j];
    }
    if (a[i]%2 != ball%2) {
      put[i] = 1;
      ball_sum++;
    } else {
      put[i] = 0;
    }
  }
  printf("%d\n", ball_sum);
  for (int i = 1; i <= n; i++) {
    if (put[i] == 1) {
      ball_sum--;
      if (ball_sum > 0) {
        printf("%d ", i);
      } else {
        printf("%d\n", i);
      }
    }
  }

  return 0;
}```

Unoptimized Assembly Code:

```assembly
	.file	"temp.c"
	.text
	.section	.rodata
.LC0:
	.string	"%d"
.LC1:
	.string	"%d\n"
.LC2:
	.string	"%d "
	.text
	.globl	main
	.type	main, @function
main:
.LFB0:
	.cfi_startproc
	endbr64
	pushq	%rbp
	.cfi_def_cfa_offset 16
	.cfi_offset 6, -16
	movq	%rsp, %rbp
	.cfi_def_cfa_register 6
	pushq	%r15
	pushq	%r14
	pushq	%r13
	pushq	%r12
	pushq	%rbx
	subq	$120, %rsp
	.cfi_offset 15, -24
	.cfi_offset 14, -32
	.cfi_offset 13, -40
	.cfi_offset 12, -48
	.cfi_offset 3, -56
	movq	%fs:40, %rax
	movq	%rax, -56(%rbp)
	xorl	%eax, %eax
	movq	%rsp, %rax
	movq	%rax, %rbx
	leaq	-116(%rbp), %rax
	movq	%rax, %rsi
	leaq	.LC0(%rip), %rax
	movq	%rax, %rdi
	movl	$0, %eax
	call	__isoc99_scanf@PLT
	movl	-116(%rbp), %eax
	addl	$1, %eax
	movslq	%eax, %rdx
	subq	$1, %rdx
	movq	%rdx, -88(%rbp)
	movslq	%eax, %rdx
	movq	%rdx, -144(%rbp)
	movq	$0, -136(%rbp)
	movslq	%eax, %rdx
	movq	%rdx, -160(%rbp)
	movq	$0, -152(%rbp)
	cltq
	leaq	0(,%rax,4), %rdx
	movl	$16, %eax
	subq	$1, %rax
	addq	%rdx, %rax
	movl	$16, %esi
	movl	$0, %edx
	divq	%rsi
	imulq	$16, %rax, %rax
	movq	%rax, %rcx
	andq	$-4096, %rcx
	movq	%rsp, %rdx
	subq	%rcx, %rdx
.L2:
	cmpq	%rdx, %rsp
	je	.L3
	subq	$4096, %rsp
	orq	$0, 4088(%rsp)
	jmp	.L2
.L3:
	movq	%rax, %rdx
	andl	$4095, %edx
	subq	%rdx, %rsp
	movq	%rax, %rdx
	andl	$4095, %edx
	testq	%rdx, %rdx
	je	.L4
	andl	$4095, %eax
	subq	$8, %rax
	addq	%rsp, %rax
	orq	$0, (%rax)
.L4:
	movq	%rsp, %rax
	addq	$3, %rax
	shrq	$2, %rax
	salq	$2, %rax
	movq	%rax, -80(%rbp)
	movl	$1, -112(%rbp)
	jmp	.L5
.L6:
	movl	-112(%rbp), %eax
	cltq
	leaq	0(,%rax,4), %rdx
	movq	-80(%rbp), %rax
	addq	%rdx, %rax
	movq	%rax, %rsi
	leaq	.LC0(%rip), %rax
	movq	%rax, %rdi
	movl	$0, %eax
	call	__isoc99_scanf@PLT
	addl	$1, -112(%rbp)
.L5:
	movl	-116(%rbp), %eax
	cmpl	%eax, -112(%rbp)
	jle	.L6
	movl	-116(%rbp), %eax
	addl	$1, %eax
	movslq	%eax, %rdx
	subq	$1, %rdx
	movq	%rdx, -72(%rbp)
	movslq	%eax, %rdx
	movq	%rdx, %r14
	movl	$0, %r15d
	movslq	%eax, %rdx
	movq	%rdx, %r12
	movl	$0, %r13d
	cltq
	leaq	0(,%rax,4), %rdx
	movl	$16, %eax
	subq	$1, %rax
	addq	%rdx, %rax
	movl	$16, %edi
	movl	$0, %edx
	divq	%rdi
	imulq	$16, %rax, %rax
	movq	%rax, %rcx
	andq	$-4096, %rcx
	movq	%rsp, %rdx
	subq	%rcx, %rdx
.L7:
	cmpq	%rdx, %rsp
	je	.L8
	subq	$4096, %rsp
	orq	$0, 4088(%rsp)
	jmp	.L7
.L8:
	movq	%rax, %rdx
	andl	$4095, %edx
	subq	%rdx, %rsp
	movq	%rax, %rdx
	andl	$4095, %edx
	testq	%rdx, %rdx
	je	.L9
	andl	$4095, %eax
	subq	$8, %rax
	addq	%rsp, %rax
	orq	$0, (%rax)
.L9:
	movq	%rsp, %rax
	addq	$3, %rax
	shrq	$2, %rax
	salq	$2, %rax
	movq	%rax, -64(%rbp)
	movl	$0, -104(%rbp)
	movl	-116(%rbp), %eax
	movl	%eax, -100(%rbp)
	jmp	.L10
.L15:
	movl	$0, -108(%rbp)
	movl	$2, -96(%rbp)
	jmp	.L11
.L12:
	movl	-100(%rbp), %eax
	imull	-96(%rbp), %eax
	movl	%eax, %edx
	movq	-64(%rbp), %rax
	movslq	%edx, %rdx
	movl	(%rax,%rdx,4), %eax
	addl	%eax, -108(%rbp)
	addl	$1, -96(%rbp)
.L11:
	movl	-100(%rbp), %eax
	imull	-96(%rbp), %eax
	movl	%eax, %edx
	movl	-116(%rbp), %eax
	cmpl	%eax, %edx
	jle	.L12
	movq	-80(%rbp), %rax
	movl	-100(%rbp), %edx
	movslq	%edx, %rdx
	movl	(%rax,%rdx,4), %eax
	cltd
	shrl	$31, %edx
	addl	%edx, %eax
	andl	$1, %eax
	subl	%edx, %eax
	movl	%eax, %ecx
	movl	-108(%rbp), %eax
	cltd
	shrl	$31, %edx
	addl	%edx, %eax
	andl	$1, %eax
	subl	%edx, %eax
	cmpl	%eax, %ecx
	je	.L13
	movq	-64(%rbp), %rax
	movl	-100(%rbp), %edx
	movslq	%edx, %rdx
	movl	$1, (%rax,%rdx,4)
	addl	$1, -104(%rbp)
	jmp	.L14
.L13:
	movq	-64(%rbp), %rax
	movl	-100(%rbp), %edx
	movslq	%edx, %rdx
	movl	$0, (%rax,%rdx,4)
.L14:
	subl	$1, -100(%rbp)
.L10:
	cmpl	$0, -100(%rbp)
	jg	.L15
	movl	-104(%rbp), %eax
	movl	%eax, %esi
	leaq	.LC1(%rip), %rax
	movq	%rax, %rdi
	movl	$0, %eax
	call	printf@PLT
	movl	$1, -92(%rbp)
	jmp	.L16
.L19:
	movq	-64(%rbp), %rax
	movl	-92(%rbp), %edx
	movslq	%edx, %rdx
	movl	(%rax,%rdx,4), %eax
	cmpl	$1, %eax
	jne	.L17
	subl	$1, -104(%rbp)
	cmpl	$0, -104(%rbp)
	jle	.L18
	movl	-92(%rbp), %eax
	movl	%eax, %esi
	leaq	.LC2(%rip), %rax
	movq	%rax, %rdi
	movl	$0, %eax
	call	printf@PLT
	jmp	.L17
.L18:
	movl	-92(%rbp), %eax
	movl	%eax, %esi
	leaq	.LC1(%rip), %rax
	movq	%rax, %rdi
	movl	$0, %eax
	call	printf@PLT
.L17:
	addl	$1, -92(%rbp)
.L16:
	movl	-116(%rbp), %eax
	cmpl	%eax, -92(%rbp)
	jle	.L19
	movl	$0, %eax
	movq	%rbx, %rsp
	movq	-56(%rbp), %rdx
	subq	%fs:40, %rdx
	je	.L21
	call	__stack_chk_fail@PLT
.L21:
	leaq	-40(%rbp), %rsp
	popq	%rbx
	popq	%r12
	popq	%r13
	popq	%r14
	popq	%r15
	popq	%rbp
	.cfi_def_cfa 7, 8
	ret
	.cfi_endproc
.LFE0:
	.size	main, .-main
	.ident	"GCC: (Ubuntu 11.4.0-1ubuntu1~22.04) 11.4.0"
	.section	.note.GNU-stack,"",@progbits
	.section	.note.gnu.property,"a"
	.align 8
	.long	1f - 0f
	.long	4f - 1f
	.long	5
0:
	.string	"GNU"
1:
	.align 8
	.long	0xc0000002
	.long	3f - 2f
2:
	.long	0x3
3:
	.align 8
4:
```

Only output the optimized assembly code. Do not include any other text. Do not write any comments in the assembly code. Wrap the assembly code in ```assembly``` tags.
user
	.file	"temp.c"
	.text
	.section	.rodata.str1.1,"aMS",@progbits,1
.LC0:
	.string	"%d"
.LC1:
	.string	"%d\n"
.LC2:
	.string	"%d "
	.section	.text.startup,"ax",@progbits
	.p2align 4
	.globl	main
	.type	main, @function
main:
.LFB23:
	.cfi_startproc
	endbr64
	pushq	%rbp
	.cfi_def_cfa_offset 16
	.cfi_offset 6, -16
	movq	%rsp, %rbp
	.cfi_def_cfa_register 6
	pushq	%r15
	pushq	%r14
	.cfi_offset 15, -24
	.cfi_offset 14, -32
	leaq	.LC0(%rip), %r14
	leaq	-60(%rbp), %rsi
	pushq	%r13
	movq	%r14, %rdi
	pushq	%r12
	pushq	%rbx
	subq	$24, %rsp
	.cfi_offset 13, -40
	.cfi_offset 12, -48
	.cfi_offset 3, -56
	movq	%fs:40, %rax
	movq	%rax, -56(%rbp)
	xorl	%eax, %eax
	call	__isoc99_scanf@PLT
	movl	-60(%rbp), %ecx
	movq	%rsp, %rsi
	leal	1(%rcx), %eax
	cltq
	leaq	15(,%rax,4), %rax
	movq	%rax, %rdi
	movq	%rax, %rdx
	andq	$-4096, %rdi
	andq	$-16, %rdx
	subq	%rdi, %rsi
	cmpq	%rsi, %rsp
	je	.L3
.L47:
	subq	$4096, %rsp
	orq	$0, 4088(%rsp)
	cmpq	%rsi, %rsp
	jne	.L47
.L3:
	andl	$4095, %edx
	subq	%rdx, %rsp
	testq	%rdx, %rdx
	jne	.L48
.L4:
	movq	%rsp, %r13
	testl	%ecx, %ecx
	jle	.L5
	leaq	4(%r13), %r12
	movl	$1, %ebx
	.p2align 4,,10
	.p2align 3
.L6:
	movq	%r12, %rsi
	movq	%r14, %rdi
	xorl	%eax, %eax
	addl	$1, %ebx
	call	__isoc99_scanf@PLT
	movl	-60(%rbp), %esi
	addq	$4, %r12
	cmpl	%ebx, %esi
	jge	.L6
	leal	1(%rsi), %eax
	movq	%rsp, %rcx
	cltq
	leaq	15(,%rax,4), %rax
	movq	%rax, %rdx
	andq	$-4096, %rax
	andq	$-16, %rdx
	subq	%rax, %rcx
.L7:
	cmpq	%rcx, %rsp
	je	.L8
	subq	$4096, %rsp
	orq	$0, 4088(%rsp)
	jmp	.L7
.L8:
	andl	$4095, %edx
	subq	%rdx, %rsp
	testq	%rdx, %rdx
	jne	.L49
.L9:
	movq	%rsp, %rdi
	movq	%rdi, %r12
	testl	%esi, %esi
	jle	.L24
	movslq	%esi, %rcx
	leal	(%rsi,%rsi), %r8d
	xorl	%ebx, %ebx
	.p2align 4,,10
	.p2align 3
.L11:
	leaq	(%rcx,%rcx), %rax
	xorl	%edx, %edx
	cmpl	%r8d, %esi
	jl	.L15
	.p2align 4,,10
	.p2align 3
.L12:
	addl	(%rdi,%rax,4), %edx
	addq	%rcx, %rax
	cmpl	%eax, %esi
	jge	.L12
	movl	%edx, %eax
	shrl	$31, %eax
	addl	%eax, %edx
	andl	$1, %edx
	subl	%eax, %edx
.L15:
	movl	0(%r13,%rcx,4), %eax
	movl	%eax, %r9d
	shrl	$31, %r9d
	addl	%r9d, %eax
	andl	$1, %eax
	subl	%r9d, %eax
	xorl	%r9d, %r9d
	cmpl	%edx, %eax
	je	.L13
	addl	$1, %ebx
	movl	$1, %r9d
.L13:
	movl	%r9d, (%rdi,%rcx,4)
	subq	$1, %rcx
	subl	$2, %r8d
	jne	.L11
.L10:
	leaq	.LC1(%rip), %r14
	movl	%ebx, %edx
	movl	$1, %edi
	xorl	%eax, %eax
	movq	%r14, %rsi
	movl	$1, %r13d
	leaq	.LC2(%rip), %r15
	call	__printf_chk@PLT
	movl	-60(%rbp), %eax
	testl	%eax, %eax
	jg	.L16
	jmp	.L19
	.p2align 4,,10
	.p2align 3
.L17:
	addq	$1, %r13
	cmpl	%r13d, %eax
	jl	.L19
.L16:
	cmpl	$1, (%r12,%r13,4)
	movl	%r13d, %edx
	jne	.L17
	subl	$1, %ebx
	testl	%ebx, %ebx
	jle	.L18
	movq	%r15, %rsi
	movl	$1, %edi
	xorl	%eax, %eax
	addq	$1, %r13
	call	__printf_chk@PLT
	movl	-60(%rbp), %eax
	cmpl	%r13d, %eax
	jge	.L16
	.p2align 4,,10
	.p2align 3
.L19:
	movq	-56(%rbp), %rax
	subq	%fs:40, %rax
	jne	.L50
	leaq	-40(%rbp), %rsp
	xorl	%eax, %eax
	popq	%rbx
	popq	%r12
	popq	%r13
	popq	%r14
	popq	%r15
	popq	%rbp
	.cfi_remember_state
	.cfi_def_cfa 7, 8
	ret
	.p2align 4,,10
	.p2align 3
.L18:
	.cfi_restore_state
	movq	%r14, %rsi
	movl	$1, %edi
	xorl	%eax, %eax
	call	__printf_chk@PLT
	movl	-60(%rbp), %eax
	jmp	.L17
.L48:
	orq	$0, -8(%rsp,%rdx)
	jmp	.L4
.L49:
	orq	$0, -8(%rsp,%rdx)
	jmp	.L9
.L5:
	movq	%rax, %rdx
	movq	%rsp, %rcx
	andq	$-4096, %rax
	andq	$-16, %rdx
	subq	%rax, %rcx
.L20:
	cmpq	%rcx, %rsp
	je	.L21
	subq	$4096, %rsp
	orq	$0, 4088(%rsp)
	jmp	.L20
.L21:
	movq	%rdx, %rax
	andl	$4095, %eax
	subq	%rax, %rsp
	testq	%rax, %rax
	je	.L22
	orq	$0, -8(%rsp,%rax)
.L22:
	movq	%rsp, %r12
	xorl	%ebx, %ebx
	jmp	.L10
.L24:
	xorl	%ebx, %ebx
	jmp	.L10
.L50:
	call	__stack_chk_fail@PLT
	.cfi_endproc
.LFE23:
	.size	main, .-main
	.ident	"GCC: (Ubuntu 11.4.0-1ubuntu1~22.04) 11.4.0"
	.section	.note.GNU-stack,"",@progbits
	.section	.note.gnu.property,"a"
	.align 8
	.long	1f - 0f
	.long	4f - 1f
	.long	5
0:
	.string	"GNU"
1:
	.align 8
	.long	0xc0000002
	.long	3f - 2f
2:
	.long	0x3
3:
	.align 8
4:

rule
	.file	"temp.c"
	.text
	.section	.rodata.str1.1,"aMS",@progbits,1
.LC0:
	.string	"%d"
.LC1:
	.string	"%d\n"
.LC2:
	.string	"%d "
	.section	.text.startup,"ax",@progbits
	.p2align 4
	.globl	main
	.type	main, @function
main:
.LFB23:
	.cfi_startproc
	endbr64
	pushq	%rbp
	.cfi_def_cfa_offset 16
	.cfi_offset 6, -16
	movq	%rsp, %rbp
	.cfi_def_cfa_register 6
	pushq	%r15
	pushq	%r14
	.cfi_offset 15, -24
	.cfi_offset 14, -32
	leaq	.LC0(%rip), %r14
	leaq	-60(%rbp), %rsi
	pushq	%r13
	movq	%r14, %rdi
	pushq	%r12
	pushq	%rbx
	subq	$24, %rsp
	.cfi_offset 13, -40
	.cfi_offset 12, -48
	.cfi_offset 3, -56
	movq	%fs:40, %rax
	movq	%rax, -56(%rbp)
	xorl	%eax, %eax
	call	__isoc99_scanf@PLT
	movl	-60(%rbp), %ecx
	movq	%rsp, %rsi
	leal	1(%rcx), %eax
	cltq
	leaq	15(,%rax,4), %rax
	movq	%rax, %rdi
	movq	%rax, %rdx
	andq	$-4096, %rdi
	andq	$-16, %rdx
	subq	%rdi, %rsi
	cmpq	%rsi, %rsp
	je	.L3
.L47:
	subq	$4096, %rsp
	orq	$0, 4088(%rsp)
	cmpq	%rsi, %rsp
	jne	.L47
.L3:
	andl	$4095, %edx
	subq	%rdx, %rsp
	testq	%rdx, %rdx
	jne	.L48
.L4:
	movq	%rsp, %r13
	testl	%ecx, %ecx
	jle	.L5
	leaq	4(%r13), %r12
	movl	$1, %ebx
	.p2align 4,,10
	.p2align 3
.L6:
	movq	%r12, %rsi
	movq	%r14, %rdi
	xorl	%eax, %eax
	addl	$1, %ebx
	call	__isoc99_scanf@PLT
	movl	-60(%rbp), %esi
	addq	$4, %r12
	cmpl	%ebx, %esi
	jge	.L6
	leal	1(%rsi), %eax
	movq	%rsp, %rcx
	cltq
	leaq	15(,%rax,4), %rax
	movq	%rax, %rdx
	andq	$-4096, %rax
	andq	$-16, %rdx
	subq	%rax, %rcx
.L7:
	cmpq	%rcx, %rsp
	je	.L8
	subq	$4096, %rsp
	orq	$0, 4088(%rsp)
	jmp	.L7
.L8:
	andl	$4095, %edx
	subq	%rdx, %rsp
	testq	%rdx, %rdx
	jne	.L49
.L9:
	movq	%rsp, %rdi
	movq	%rdi, %r12
	testl	%esi, %esi
	jle	.L24
	movslq	%esi, %rcx
	leal	(%rsi,%rsi), %r8d
	xorl	%ebx, %ebx
	.p2align 4,,10
	.p2align 3
.L11:
	leaq	(%rcx,%rcx), %rax
	xorl	%edx, %edx
	cmpl	%r8d, %esi
	jl	.L15
	.p2align 4,,10
	.p2align 3
.L12:
	addl	(%rdi,%rax,4), %edx
	addq	%rcx, %rax
	cmpl	%eax, %esi
	jge	.L12
	movl	%edx, %eax
	shrl	$31, %eax
	addl	%eax, %edx
	andl	$1, %edx
	subl	%eax, %edx
.L15:
	movl	0(%r13,%rcx,4), %eax
	movl	%eax, %r9d
	shrl	$31, %r9d
	addl	%r9d, %eax
	andl	$1, %eax
	subl	%r9d, %eax
	xorl	%r9d, %r9d
	cmpl	%edx, %eax
	je	.L13
	addl	$1, %ebx
	movl	$1, %r9d
.L13:
	movl	%r9d, (%rdi,%rcx,4)
	subq	$1, %rcx
	subl	$2, %r8d
	jne	.L11
.L10:
	leaq	.LC1(%rip), %r14
	movl	%ebx, %edx
	movl	$1, %edi
	xorl	%eax, %eax
	movq	%r14, %rsi
	movl	$1, %r13d
	leaq	.LC2(%rip), %r15
	call	__printf_chk@PLT
	movl	-60(%rbp), %eax
	testl	%eax, %eax
	jg	.L16
	jmp	.L19
	.p2align 4,,10
	.p2align 3
.L17:
	addq	$1, %r13
	cmpl	%r13d, %eax
	jl	.L19
.L16:
	cmpl	$1, (%r12,%r13,4)
	movl	%r13d, %edx
	jne	.L17
	subl	$1, %ebx
	testl	%ebx, %ebx
	jle	.L18
	movq	%r15, %rsi
	movl	$1, %edi
	xorl	%eax, %eax
	addq	$1, %r13
	call	__printf_chk@PLT
	movl	-60(%rbp), %eax
	cmpl	%r13d, %eax
	jge	.L16
	.p2align 4,,10
	.p2align 3
.L19:
	movq	-56(%rbp), %rax
	subq	%fs:40, %rax
	jne	.L50
	leaq	-40(%rbp), %rsp
	xorl	%eax, %eax
	popq	%rbx
	popq	%r12
	popq	%r13
	popq	%r14
	popq	%r15
	popq	%rbp
	.cfi_remember_state
	.cfi_def_cfa 7, 8
	ret
	.p2align 4,,10
	.p2align 3
.L18:
	.cfi_restore_state
	movq	%r14, %rsi
	movl	$1, %edi
	xorl	%eax, %eax
	call	__printf_chk@PLT
	movl	-60(%rbp), %eax
	jmp	.L17
.L48:
	orq	$0, -8(%rsp,%rdx)
	jmp	.L4
.L49:
	orq	$0, -8(%rsp,%rdx)
	jmp	.L9
.L5:
	movq	%rax, %rdx
	movq	%rsp, %rcx
	andq	$-4096, %rax
	andq	$-16, %rdx
	subq	%rax, %rcx
.L20:
	cmpq	%rcx, %rsp
	je	.L21
	subq	$4096, %rsp
	orq	$0, 4088(%rsp)
	jmp	.L20
.L21:
	movq	%rdx, %rax
	andl	$4095, %eax
	subq	%rax, %rsp
	testq	%rax, %rax
	je	.L22
	orq	$0, -8(%rsp,%rax)
.L22:
	movq	%rsp, %r12
	xorl	%ebx, %ebx
	jmp	.L10
.L24:
	xorl	%ebx, %ebx
	jmp	.L10
.L50:
	call	__stack_chk_fail@PLT
	.cfi_endproc
.LFE23:
	.size	main, .-main
	.ident	"GCC: (Ubuntu 11.4.0-1ubuntu1~22.04) 11.4.0"
	.section	.note.GNU-stack,"",@progbits
	.section	.note.gnu.property,"a"
	.align 8
	.long	1f - 0f
	.long	4f - 1f
	.long	5
0:
	.string	"GNU"
1:
	.align 8
	.long	0xc0000002
	.long	3f - 2f
2:
	.long	0x3
3:
	.align 8
4:

#include <stdio.h>

int main(void) {

  int n;
  scanf("%d", &n);
  int a[n+1];
  for (int i = 1; i <= n; i++) {
    scanf("%d", &a[i]);
  }
  int put[n+1];
  int ball;
  int ball_sum = 0;
  for (int i = n; i > 0; i--) {
    ball = 0;
    for (int j = 2; i*j <= n; j++) {
      ball += put[i*j];
    }
    if (a[i]%2 != ball%2) {
      put[i] = 1;
      ball_sum++;
    } else {
      put[i] = 0;
    }
  }
  printf("%d\n", ball_sum);
  for (int i = 1; i <= n; i++) {
    if (put[i] == 1) {
      ball_sum--;
      if (ball_sum > 0) {
        printf("%d ", i);
      } else {
        printf("%d\n", i);
      }
    }
  }

  return 0;
}
3
1 0 1
 3
1 1 0
 3
0 0 0
 5
1 0 0 0 0
 5
1 0 0 0 1
 5
1 1 0 1 0
 5
1 0 1 0 0
 5
1 1 0 0 0
 5
1 0 0 0 0
 3
0 0 0

1
3
 1
2
 0
 1
1
 1
5
 1
4
 1
3
 1
2
 1
1
 0

Given the following C code and unoptimized assembly code, your task is to generate highly optimized x86-64 assembly code.
C Code:

```c
#include <stdio.h>

int main(void) {

  int n;
  scanf("%d", &n);
  int a[n+1];
  for (int i = 1; i <= n; i++) {
    scanf("%d", &a[i]);
  }
  int put[n+1];
  int ball;
  int ball_sum = 0;
  for (int i = n; i > 0; i--) {
    ball = 0;
    for (int j = 2; i*j <= n; j++) {
      ball += put[i*j];
    }
    if (a[i]%2 != ball%2) {
      put[i] = 1;
      ball_sum++;
    } else {
      put[i] = 0;
    }
  }
  printf("%d\n", ball_sum);
  for (int i = 1; i <= n; i++) {
    if (put[i] == 1) {
      ball_sum--;
      if (ball_sum > 0) {
        printf("%d ", i);
      } else {
        printf("%d\n", i);
      }
    }
  }

  return 0;
}```

Unoptimized Assembly Code:

```assembly
	.file	"temp.c"
	.text
	.section	.rodata
.LC0:
	.string	"%d"
.LC1:
	.string	"%d\n"
.LC2:
	.string	"%d "
	.text
	.globl	main
	.type	main, @function
main:
.LFB0:
	.cfi_startproc
	endbr64
	pushq	%rbp
	.cfi_def_cfa_offset 16
	.cfi_offset 6, -16
	movq	%rsp, %rbp
	.cfi_def_cfa_register 6
	pushq	%r15
	pushq	%r14
	pushq	%r13
	pushq	%r12
	pushq	%rbx
	subq	$120, %rsp
	.cfi_offset 15, -24
	.cfi_offset 14, -32
	.cfi_offset 13, -40
	.cfi_offset 12, -48
	.cfi_offset 3, -56
	movq	%fs:40, %rax
	movq	%rax, -56(%rbp)
	xorl	%eax, %eax
	movq	%rsp, %rax
	movq	%rax, %rbx
	leaq	-116(%rbp), %rax
	movq	%rax, %rsi
	leaq	.LC0(%rip), %rax
	movq	%rax, %rdi
	movl	$0, %eax
	call	__isoc99_scanf@PLT
	movl	-116(%rbp), %eax
	addl	$1, %eax
	movslq	%eax, %rdx
	subq	$1, %rdx
	movq	%rdx, -88(%rbp)
	movslq	%eax, %rdx
	movq	%rdx, -144(%rbp)
	movq	$0, -136(%rbp)
	movslq	%eax, %rdx
	movq	%rdx, -160(%rbp)
	movq	$0, -152(%rbp)
	cltq
	leaq	0(,%rax,4), %rdx
	movl	$16, %eax
	subq	$1, %rax
	addq	%rdx, %rax
	movl	$16, %esi
	movl	$0, %edx
	divq	%rsi
	imulq	$16, %rax, %rax
	movq	%rax, %rcx
	andq	$-4096, %rcx
	movq	%rsp, %rdx
	subq	%rcx, %rdx
.L2:
	cmpq	%rdx, %rsp
	je	.L3
	subq	$4096, %rsp
	orq	$0, 4088(%rsp)
	jmp	.L2
.L3:
	movq	%rax, %rdx
	andl	$4095, %edx
	subq	%rdx, %rsp
	movq	%rax, %rdx
	andl	$4095, %edx
	testq	%rdx, %rdx
	je	.L4
	andl	$4095, %eax
	subq	$8, %rax
	addq	%rsp, %rax
	orq	$0, (%rax)
.L4:
	movq	%rsp, %rax
	addq	$3, %rax
	shrq	$2, %rax
	salq	$2, %rax
	movq	%rax, -80(%rbp)
	movl	$1, -112(%rbp)
	jmp	.L5
.L6:
	movl	-112(%rbp), %eax
	cltq
	leaq	0(,%rax,4), %rdx
	movq	-80(%rbp), %rax
	addq	%rdx, %rax
	movq	%rax, %rsi
	leaq	.LC0(%rip), %rax
	movq	%rax, %rdi
	movl	$0, %eax
	call	__isoc99_scanf@PLT
	addl	$1, -112(%rbp)
.L5:
	movl	-116(%rbp), %eax
	cmpl	%eax, -112(%rbp)
	jle	.L6
	movl	-116(%rbp), %eax
	addl	$1, %eax
	movslq	%eax, %rdx
	subq	$1, %rdx
	movq	%rdx, -72(%rbp)
	movslq	%eax, %rdx
	movq	%rdx, %r14
	movl	$0, %r15d
	movslq	%eax, %rdx
	movq	%rdx, %r12
	movl	$0, %r13d
	cltq
	leaq	0(,%rax,4), %rdx
	movl	$16, %eax
	subq	$1, %rax
	addq	%rdx, %rax
	movl	$16, %edi
	movl	$0, %edx
	divq	%rdi
	imulq	$16, %rax, %rax
	movq	%rax, %rcx
	andq	$-4096, %rcx
	movq	%rsp, %rdx
	subq	%rcx, %rdx
.L7:
	cmpq	%rdx, %rsp
	je	.L8
	subq	$4096, %rsp
	orq	$0, 4088(%rsp)
	jmp	.L7
.L8:
	movq	%rax, %rdx
	andl	$4095, %edx
	subq	%rdx, %rsp
	movq	%rax, %rdx
	andl	$4095, %edx
	testq	%rdx, %rdx
	je	.L9
	andl	$4095, %eax
	subq	$8, %rax
	addq	%rsp, %rax
	orq	$0, (%rax)
.L9:
	movq	%rsp, %rax
	addq	$3, %rax
	shrq	$2, %rax
	salq	$2, %rax
	movq	%rax, -64(%rbp)
	movl	$0, -104(%rbp)
	movl	-116(%rbp), %eax
	movl	%eax, -100(%rbp)
	jmp	.L10
.L15:
	movl	$0, -108(%rbp)
	movl	$2, -96(%rbp)
	jmp	.L11
.L12:
	movl	-100(%rbp), %eax
	imull	-96(%rbp), %eax
	movl	%eax, %edx
	movq	-64(%rbp), %rax
	movslq	%edx, %rdx
	movl	(%rax,%rdx,4), %eax
	addl	%eax, -108(%rbp)
	addl	$1, -96(%rbp)
.L11:
	movl	-100(%rbp), %eax
	imull	-96(%rbp), %eax
	movl	%eax, %edx
	movl	-116(%rbp), %eax
	cmpl	%eax, %edx
	jle	.L12
	movq	-80(%rbp), %rax
	movl	-100(%rbp), %edx
	movslq	%edx, %rdx
	movl	(%rax,%rdx,4), %eax
	cltd
	shrl	$31, %edx
	addl	%edx, %eax
	andl	$1, %eax
	subl	%edx, %eax
	movl	%eax, %ecx
	movl	-108(%rbp), %eax
	cltd
	shrl	$31, %edx
	addl	%edx, %eax
	andl	$1, %eax
	subl	%edx, %eax
	cmpl	%eax, %ecx
	je	.L13
	movq	-64(%rbp), %rax
	movl	-100(%rbp), %edx
	movslq	%edx, %rdx
	movl	$1, (%rax,%rdx,4)
	addl	$1, -104(%rbp)
	jmp	.L14
.L13:
	movq	-64(%rbp), %rax
	movl	-100(%rbp), %edx
	movslq	%edx, %rdx
	movl	$0, (%rax,%rdx,4)
.L14:
	subl	$1, -100(%rbp)
.L10:
	cmpl	$0, -100(%rbp)
	jg	.L15
	movl	-104(%rbp), %eax
	movl	%eax, %esi
	leaq	.LC1(%rip), %rax
	movq	%rax, %rdi
	movl	$0, %eax
	call	printf@PLT
	movl	$1, -92(%rbp)
	jmp	.L16
.L19:
	movq	-64(%rbp), %rax
	movl	-92(%rbp), %edx
	movslq	%edx, %rdx
	movl	(%rax,%rdx,4), %eax
	cmpl	$1, %eax
	jne	.L17
	subl	$1, -104(%rbp)
	cmpl	$0, -104(%rbp)
	jle	.L18
	movl	-92(%rbp), %eax
	movl	%eax, %esi
	leaq	.LC2(%rip), %rax
	movq	%rax, %rdi
	movl	$0, %eax
	call	printf@PLT
	jmp	.L17
.L18:
	movl	-92(%rbp), %eax
	movl	%eax, %esi
	leaq	.LC1(%rip), %rax
	movq	%rax, %rdi
	movl	$0, %eax
	call	printf@PLT
.L17:
	addl	$1, -92(%rbp)
.L16:
	movl	-116(%rbp), %eax
	cmpl	%eax, -92(%rbp)
	jle	.L19
	movl	$0, %eax
	movq	%rbx, %rsp
	movq	-56(%rbp), %rdx
	subq	%fs:40, %rdx
	je	.L21
	call	__stack_chk_fail@PLT
.L21:
	leaq	-40(%rbp), %rsp
	popq	%rbx
	popq	%r12
	popq	%r13
	popq	%r14
	popq	%r15
	popq	%rbp
	.cfi_def_cfa 7, 8
	ret
	.cfi_endproc
.LFE0:
	.size	main, .-main
	.ident	"GCC: (Ubuntu 11.4.0-1ubuntu1~22.04) 11.4.0"
	.section	.note.GNU-stack,"",@progbits
	.section	.note.gnu.property,"a"
	.align 8
	.long	1f - 0f
	.long	4f - 1f
	.long	5
0:
	.string	"GNU"
1:
	.align 8
	.long	0xc0000002
	.long	3f - 2f
2:
	.long	0x3
3:
	.align 8
4:
```

Only output the optimized assembly code. Do not include any other text. Do not write any comments in the assembly code. Wrap the assembly code in ```assembly``` tags.
train
	.file	"temp.c"
	.text
	.section	.rodata
.LC0:
	.string	"%d"
.LC1:
	.string	"%d\n"
.LC2:
	.string	"%d "
	.text
	.globl	main
	.type	main, @function
main:
.LFB0:
	.cfi_startproc
	endbr64
	pushq	%rbp
	.cfi_def_cfa_offset 16
	.cfi_offset 6, -16
	movq	%rsp, %rbp
	.cfi_def_cfa_register 6
	pushq	%r15
	pushq	%r14
	pushq	%r13
	pushq	%r12
	pushq	%rbx
	subq	$120, %rsp
	.cfi_offset 15, -24
	.cfi_offset 14, -32
	.cfi_offset 13, -40
	.cfi_offset 12, -48
	.cfi_offset 3, -56
	movq	%fs:40, %rax
	movq	%rax, -56(%rbp)
	xorl	%eax, %eax
	movq	%rsp, %rax
	movq	%rax, %rbx
	leaq	-116(%rbp), %rax
	movq	%rax, %rsi
	leaq	.LC0(%rip), %rax
	movq	%rax, %rdi
	movl	$0, %eax
	call	__isoc99_scanf@PLT
	movl	-116(%rbp), %eax
	addl	$1, %eax
	movslq	%eax, %rdx
	subq	$1, %rdx
	movq	%rdx, -88(%rbp)
	movslq	%eax, %rdx
	movq	%rdx, -144(%rbp)
	movq	$0, -136(%rbp)
	movslq	%eax, %rdx
	movq	%rdx, -160(%rbp)
	movq	$0, -152(%rbp)
	cltq
	leaq	0(,%rax,4), %rdx
	movl	$16, %eax
	subq	$1, %rax
	addq	%rdx, %rax
	movl	$16, %esi
	movl	$0, %edx
	divq	%rsi
	imulq	$16, %rax, %rax
	movq	%rax, %rcx
	andq	$-4096, %rcx
	movq	%rsp, %rdx
	subq	%rcx, %rdx
.L2:
	cmpq	%rdx, %rsp
	je	.L3
	subq	$4096, %rsp
	orq	$0, 4088(%rsp)
	jmp	.L2
.L3:
	movq	%rax, %rdx
	andl	$4095, %edx
	subq	%rdx, %rsp
	movq	%rax, %rdx
	andl	$4095, %edx
	testq	%rdx, %rdx
	je	.L4
	andl	$4095, %eax
	subq	$8, %rax
	addq	%rsp, %rax
	orq	$0, (%rax)
.L4:
	movq	%rsp, %rax
	addq	$3, %rax
	shrq	$2, %rax
	salq	$2, %rax
	movq	%rax, -80(%rbp)
	movl	$1, -112(%rbp)
	jmp	.L5
.L6:
	movl	-112(%rbp), %eax
	cltq
	leaq	0(,%rax,4), %rdx
	movq	-80(%rbp), %rax
	addq	%rdx, %rax
	movq	%rax, %rsi
	leaq	.LC0(%rip), %rax
	movq	%rax, %rdi
	movl	$0, %eax
	call	__isoc99_scanf@PLT
	addl	$1, -112(%rbp)
.L5:
	movl	-116(%rbp), %eax
	cmpl	%eax, -112(%rbp)
	jle	.L6
	movl	-116(%rbp), %eax
	addl	$1, %eax
	movslq	%eax, %rdx
	subq	$1, %rdx
	movq	%rdx, -72(%rbp)
	movslq	%eax, %rdx
	movq	%rdx, %r14
	movl	$0, %r15d
	movslq	%eax, %rdx
	movq	%rdx, %r12
	movl	$0, %r13d
	cltq
	leaq	0(,%rax,4), %rdx
	movl	$16, %eax
	subq	$1, %rax
	addq	%rdx, %rax
	movl	$16, %edi
	movl	$0, %edx
	divq	%rdi
	imulq	$16, %rax, %rax
	movq	%rax, %rcx
	andq	$-4096, %rcx
	movq	%rsp, %rdx
	subq	%rcx, %rdx
.L7:
	cmpq	%rdx, %rsp
	je	.L8
	subq	$4096, %rsp
	orq	$0, 4088(%rsp)
	jmp	.L7
.L8:
	movq	%rax, %rdx
	andl	$4095, %edx
	subq	%rdx, %rsp
	movq	%rax, %rdx
	andl	$4095, %edx
	testq	%rdx, %rdx
	je	.L9
	andl	$4095, %eax
	subq	$8, %rax
	addq	%rsp, %rax
	orq	$0, (%rax)
.L9:
	movq	%rsp, %rax
	addq	$3, %rax
	shrq	$2, %rax
	salq	$2, %rax
	movq	%rax, -64(%rbp)
	movl	$0, -104(%rbp)
	movl	-116(%rbp), %eax
	movl	%eax, -100(%rbp)
	jmp	.L10
.L15:
	movl	$0, -108(%rbp)
	movl	$2, -96(%rbp)
	jmp	.L11
.L12:
	movl	-100(%rbp), %eax
	imull	-96(%rbp), %eax
	movl	%eax, %edx
	movq	-64(%rbp), %rax
	movslq	%edx, %rdx
	movl	(%rax,%rdx,4), %eax
	addl	%eax, -108(%rbp)
	addl	$1, -96(%rbp)
.L11:
	movl	-100(%rbp), %eax
	imull	-96(%rbp), %eax
	movl	%eax, %edx
	movl	-116(%rbp), %eax
	cmpl	%eax, %edx
	jle	.L12
	movq	-80(%rbp), %rax
	movl	-100(%rbp), %edx
	movslq	%edx, %rdx
	movl	(%rax,%rdx,4), %eax
	cltd
	shrl	$31, %edx
	addl	%edx, %eax
	andl	$1, %eax
	subl	%edx, %eax
	movl	%eax, %ecx
	movl	-108(%rbp), %eax
	cltd
	shrl	$31, %edx
	addl	%edx, %eax
	andl	$1, %eax
	subl	%edx, %eax
	cmpl	%eax, %ecx
	je	.L13
	movq	-64(%rbp), %rax
	movl	-100(%rbp), %edx
	movslq	%edx, %rdx
	movl	$1, (%rax,%rdx,4)
	addl	$1, -104(%rbp)
	jmp	.L14
.L13:
	movq	-64(%rbp), %rax
	movl	-100(%rbp), %edx
	movslq	%edx, %rdx
	movl	$0, (%rax,%rdx,4)
.L14:
	subl	$1, -100(%rbp)
.L10:
	cmpl	$0, -100(%rbp)
	jg	.L15
	movl	-104(%rbp), %eax
	movl	%eax, %esi
	leaq	.LC1(%rip), %rax
	movq	%rax, %rdi
	movl	$0, %eax
	call	printf@PLT
	movl	$1, -92(%rbp)
	jmp	.L16
.L19:
	movq	-64(%rbp), %rax
	movl	-92(%rbp), %edx
	movslq	%edx, %rdx
	movl	(%rax,%rdx,4), %eax
	cmpl	$1, %eax
	jne	.L17
	subl	$1, -104(%rbp)
	cmpl	$0, -104(%rbp)
	jle	.L18
	movl	-92(%rbp), %eax
	movl	%eax, %esi
	leaq	.LC2(%rip), %rax
	movq	%rax, %rdi
	movl	$0, %eax
	call	printf@PLT
	jmp	.L17
.L18:
	movl	-92(%rbp), %eax
	movl	%eax, %esi
	leaq	.LC1(%rip), %rax
	movq	%rax, %rdi
	movl	$0, %eax
	call	printf@PLT
.L17:
	addl	$1, -92(%rbp)
.L16:
	movl	-116(%rbp), %eax
	cmpl	%eax, -92(%rbp)
	jle	.L19
	movl	$0, %eax
	movq	%rbx, %rsp
	movq	-56(%rbp), %rdx
	subq	%fs:40, %rdx
	je	.L21
	call	__stack_chk_fail@PLT
.L21:
	leaq	-40(%rbp), %rsp
	popq	%rbx
	popq	%r12
	popq	%r13
	popq	%r14
	popq	%r15
	popq	%rbp
	.cfi_def_cfa 7, 8
	ret
	.cfi_endproc
.LFE0:
	.size	main, .-main
	.ident	"GCC: (Ubuntu 11.4.0-1ubuntu1~22.04) 11.4.0"
	.section	.note.GNU-stack,"",@progbits
	.section	.note.gnu.property,"a"
	.align 8
	.long	1f - 0f
	.long	4f - 1f
	.long	5
0:
	.string	"GNU"
1:
	.align 8
	.long	0xc0000002
	.long	3f - 2f
2:
	.long	0x3
3:
	.align 8
4:
