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

```c
i,a;main(x){for(x=scanf("%d",&a);a>3;x++)i=a%3?1:0,a/=3,a+=i;printf("%d\n",x);exit(0);}```

Unoptimized Assembly Code:

```assembly
	.file	"temp.c"
	.text
	.globl	i
	.bss
	.align 4
	.type	i, @object
	.size	i, 4
i:
	.zero	4
	.globl	a
	.align 4
	.type	a, @object
	.size	a, 4
a:
	.zero	4
	.section	.rodata
.LC0:
	.string	"%d"
.LC1:
	.string	"%d\n"
	.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
	subq	$16, %rsp
	movl	%edi, -4(%rbp)
	leaq	a(%rip), %rax
	movq	%rax, %rsi
	leaq	.LC0(%rip), %rax
	movq	%rax, %rdi
	movl	$0, %eax
	call	scanf@PLT
	movl	%eax, -4(%rbp)
	jmp	.L2
.L3:
	movl	a(%rip), %edx
	movslq	%edx, %rax
	imulq	$1431655766, %rax, %rax
	shrq	$32, %rax
	movl	%edx, %ecx
	sarl	$31, %ecx
	subl	%ecx, %eax
	movl	%eax, %ecx
	addl	%ecx, %ecx
	addl	%eax, %ecx
	movl	%edx, %eax
	subl	%ecx, %eax
	testl	%eax, %eax
	setne	%al
	movzbl	%al, %eax
	movl	%eax, i(%rip)
	movl	a(%rip), %eax
	movslq	%eax, %rdx
	imulq	$1431655766, %rdx, %rdx
	shrq	$32, %rdx
	sarl	$31, %eax
	movl	%eax, %ecx
	movl	%edx, %eax
	subl	%ecx, %eax
	movl	%eax, a(%rip)
	movl	a(%rip), %edx
	movl	i(%rip), %eax
	addl	%edx, %eax
	movl	%eax, a(%rip)
	addl	$1, -4(%rbp)
.L2:
	movl	a(%rip), %eax
	cmpl	$3, %eax
	jg	.L3
	movl	-4(%rbp), %eax
	movl	%eax, %esi
	leaq	.LC1(%rip), %rax
	movq	%rax, %rdi
	movl	$0, %eax
	call	printf@PLT
	movl	$0, %edi
	call	exit@PLT
	.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"
	.section	.text.startup,"ax",@progbits
	.p2align 4
	.globl	main
	.type	main, @function
main:
.LFB0:
	.cfi_startproc
	endbr64
	pushq	%rax
	.cfi_def_cfa_offset 16
	popq	%rax
	.cfi_def_cfa_offset 8
	leaq	a(%rip), %rsi
	leaq	.LC0(%rip), %rdi
	xorl	%eax, %eax
	subq	$8, %rsp
	.cfi_def_cfa_offset 16
	call	scanf@PLT
	movl	a(%rip), %ecx
	movl	%eax, %esi
	cmpl	$3, %ecx
	jle	.L2
	movl	$2863311531, %edi
	.p2align 4,,10
	.p2align 3
.L3:
	movl	%ecx, %edx
	imulq	%rdi, %rdx
	shrq	$33, %rdx
	leal	(%rdx,%rdx,2), %eax
	cmpl	%eax, %ecx
	setne	%al
	addl	$1, %esi
	movzbl	%al, %eax
	leal	(%rdx,%rax), %ecx
	cmpl	$3, %ecx
	jg	.L3
	movl	%eax, i(%rip)
	movl	%ecx, a(%rip)
.L2:
	leaq	.LC1(%rip), %rdi
	xorl	%eax, %eax
	call	printf@PLT
	xorl	%edi, %edi
	call	exit@PLT
	.cfi_endproc
.LFE0:
	.size	main, .-main
	.globl	a
	.bss
	.align 4
	.type	a, @object
	.size	a, 4
a:
	.zero	4
	.globl	i
	.align 4
	.type	i, @object
	.size	i, 4
i:
	.zero	4
	.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"
	.section	.text.startup,"ax",@progbits
	.p2align 4
	.globl	main
	.type	main, @function
main:
.LFB0:
	.cfi_startproc
	endbr64
	pushq	%rax
	.cfi_def_cfa_offset 16
	popq	%rax
	.cfi_def_cfa_offset 8
	leaq	a(%rip), %rsi
	leaq	.LC0(%rip), %rdi
	xorl	%eax, %eax
	subq	$8, %rsp
	.cfi_def_cfa_offset 16
	call	scanf@PLT
	movl	a(%rip), %ecx
	movl	%eax, %esi
	cmpl	$3, %ecx
	jle	.L2
	movl	$2863311531, %edi
	.p2align 4,,10
	.p2align 3
.L3:
	movl	%ecx, %edx
	imulq	%rdi, %rdx
	shrq	$33, %rdx
	leal	(%rdx,%rdx,2), %eax
	cmpl	%eax, %ecx
	setne	%al
	addl	$1, %esi
	movzbl	%al, %eax
	leal	(%rdx,%rax), %ecx
	cmpl	$3, %ecx
	jg	.L3
	movl	%eax, i(%rip)
	movl	%ecx, a(%rip)
.L2:
	leaq	.LC1(%rip), %rdi
	xorl	%eax, %eax
	call	printf@PLT
	xorl	%edi, %edi
	call	exit@PLT
	.cfi_endproc
.LFE0:
	.size	main, .-main
	.globl	a
	.bss
	.align 4
	.type	a, @object
	.size	a, 4
a:
	.zero	4
	.globl	i
	.align 4
	.type	i, @object
	.size	i, 4
i:
	.zero	4
	.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:

i,a;main(x){for(x=scanf("%d",&a);a>3;x++)i=a%3?1:0,a/=3,a+=i;printf("%d\n",x);exit(0);}
57
 13
 1204648530
 3
 5
 22801121
 11933788
 2291365
 784277
 166022

4
 3
 20
 1
 2
 16
 15
 14
 13
 11

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

```c
i,a;main(x){for(x=scanf("%d",&a);a>3;x++)i=a%3?1:0,a/=3,a+=i;printf("%d\n",x);exit(0);}```

Unoptimized Assembly Code:

```assembly
	.file	"temp.c"
	.text
	.globl	i
	.bss
	.align 4
	.type	i, @object
	.size	i, 4
i:
	.zero	4
	.globl	a
	.align 4
	.type	a, @object
	.size	a, 4
a:
	.zero	4
	.section	.rodata
.LC0:
	.string	"%d"
.LC1:
	.string	"%d\n"
	.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
	subq	$16, %rsp
	movl	%edi, -4(%rbp)
	leaq	a(%rip), %rax
	movq	%rax, %rsi
	leaq	.LC0(%rip), %rax
	movq	%rax, %rdi
	movl	$0, %eax
	call	scanf@PLT
	movl	%eax, -4(%rbp)
	jmp	.L2
.L3:
	movl	a(%rip), %edx
	movslq	%edx, %rax
	imulq	$1431655766, %rax, %rax
	shrq	$32, %rax
	movl	%edx, %ecx
	sarl	$31, %ecx
	subl	%ecx, %eax
	movl	%eax, %ecx
	addl	%ecx, %ecx
	addl	%eax, %ecx
	movl	%edx, %eax
	subl	%ecx, %eax
	testl	%eax, %eax
	setne	%al
	movzbl	%al, %eax
	movl	%eax, i(%rip)
	movl	a(%rip), %eax
	movslq	%eax, %rdx
	imulq	$1431655766, %rdx, %rdx
	shrq	$32, %rdx
	sarl	$31, %eax
	movl	%eax, %ecx
	movl	%edx, %eax
	subl	%ecx, %eax
	movl	%eax, a(%rip)
	movl	a(%rip), %edx
	movl	i(%rip), %eax
	addl	%edx, %eax
	movl	%eax, a(%rip)
	addl	$1, -4(%rbp)
.L2:
	movl	a(%rip), %eax
	cmpl	$3, %eax
	jg	.L3
	movl	-4(%rbp), %eax
	movl	%eax, %esi
	leaq	.LC1(%rip), %rax
	movq	%rax, %rdi
	movl	$0, %eax
	call	printf@PLT
	movl	$0, %edi
	call	exit@PLT
	.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
	.globl	i
	.bss
	.align 4
	.type	i, @object
	.size	i, 4
i:
	.zero	4
	.globl	a
	.align 4
	.type	a, @object
	.size	a, 4
a:
	.zero	4
	.section	.rodata
.LC0:
	.string	"%d"
.LC1:
	.string	"%d\n"
	.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
	subq	$16, %rsp
	movl	%edi, -4(%rbp)
	leaq	a(%rip), %rax
	movq	%rax, %rsi
	leaq	.LC0(%rip), %rax
	movq	%rax, %rdi
	movl	$0, %eax
	call	scanf@PLT
	movl	%eax, -4(%rbp)
	jmp	.L2
.L3:
	movl	a(%rip), %edx
	movslq	%edx, %rax
	imulq	$1431655766, %rax, %rax
	shrq	$32, %rax
	movl	%edx, %ecx
	sarl	$31, %ecx
	subl	%ecx, %eax
	movl	%eax, %ecx
	addl	%ecx, %ecx
	addl	%eax, %ecx
	movl	%edx, %eax
	subl	%ecx, %eax
	testl	%eax, %eax
	setne	%al
	movzbl	%al, %eax
	movl	%eax, i(%rip)
	movl	a(%rip), %eax
	movslq	%eax, %rdx
	imulq	$1431655766, %rdx, %rdx
	shrq	$32, %rdx
	sarl	$31, %eax
	movl	%eax, %ecx
	movl	%edx, %eax
	subl	%ecx, %eax
	movl	%eax, a(%rip)
	movl	a(%rip), %edx
	movl	i(%rip), %eax
	addl	%edx, %eax
	movl	%eax, a(%rip)
	addl	$1, -4(%rbp)
.L2:
	movl	a(%rip), %eax
	cmpl	$3, %eax
	jg	.L3
	movl	-4(%rbp), %eax
	movl	%eax, %esi
	leaq	.LC1(%rip), %rax
	movq	%rax, %rdi
	movl	$0, %eax
	call	printf@PLT
	movl	$0, %edi
	call	exit@PLT
	.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:
