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

```c
M=1e9+7;f[999];n;k;main(a){for(scanf("%d",f);n=*f;f[n]++,--*f)for(k=2;k*k<=n;)n%k?k++:(n/=k,f[k]++);for(;n<996;)a=1L*a*-~f[2+n++]%M;printf("%d",a);}```

Unoptimized Assembly Code:

```assembly
	.file	"temp.c"
	.text
	.globl	M
	.data
	.align 4
	.type	M, @object
	.size	M, 4
M:
	.long	1000000007
	.globl	f
	.bss
	.align 32
	.type	f, @object
	.size	f, 3996
f:
	.zero	3996
	.globl	n
	.align 4
	.type	n, @object
	.size	n, 4
n:
	.zero	4
	.globl	k
	.align 4
	.type	k, @object
	.size	k, 4
k:
	.zero	4
	.section	.rodata
.LC0:
	.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
	subq	$16, %rsp
	movl	%edi, -4(%rbp)
	leaq	f(%rip), %rax
	movq	%rax, %rsi
	leaq	.LC0(%rip), %rax
	movq	%rax, %rdi
	movl	$0, %eax
	call	scanf@PLT
	jmp	.L2
.L6:
	movl	$2, k(%rip)
	jmp	.L3
.L5:
	movl	n(%rip), %eax
	movl	k(%rip), %ecx
	cltd
	idivl	%ecx
	movl	%edx, %eax
	testl	%eax, %eax
	je	.L4
	movl	k(%rip), %eax
	addl	$1, %eax
	movl	%eax, k(%rip)
	jmp	.L3
.L4:
	movl	n(%rip), %eax
	movl	k(%rip), %esi
	cltd
	idivl	%esi
	movl	%eax, n(%rip)
	movl	k(%rip), %eax
	movslq	%eax, %rdx
	leaq	0(,%rdx,4), %rcx
	leaq	f(%rip), %rdx
	movl	(%rcx,%rdx), %edx
	leal	1(%rdx), %ecx
	cltq
	leaq	0(,%rax,4), %rdx
	leaq	f(%rip), %rax
	movl	%ecx, (%rdx,%rax)
.L3:
	movl	k(%rip), %edx
	movl	k(%rip), %eax
	imull	%eax, %edx
	movl	n(%rip), %eax
	cmpl	%eax, %edx
	jle	.L5
	movl	n(%rip), %eax
	movslq	%eax, %rdx
	leaq	0(,%rdx,4), %rcx
	leaq	f(%rip), %rdx
	movl	(%rcx,%rdx), %edx
	leal	1(%rdx), %ecx
	cltq
	leaq	0(,%rax,4), %rdx
	leaq	f(%rip), %rax
	movl	%ecx, (%rdx,%rax)
	movl	f(%rip), %eax
	subl	$1, %eax
	movl	%eax, f(%rip)
.L2:
	movl	f(%rip), %eax
	movl	%eax, n(%rip)
	movl	n(%rip), %eax
	testl	%eax, %eax
	jne	.L6
	jmp	.L7
.L8:
	movl	-4(%rbp), %eax
	movslq	%eax, %rcx
	movl	n(%rip), %eax
	leal	1(%rax), %edx
	movl	%edx, n(%rip)
	addl	$2, %eax
	cltq
	leaq	0(,%rax,4), %rdx
	leaq	f(%rip), %rax
	movl	(%rdx,%rax), %eax
	addl	$1, %eax
	cltq
	imulq	%rcx, %rax
	movl	M(%rip), %edx
	movslq	%edx, %rcx
	cqto
	idivq	%rcx
	movq	%rdx, %rax
	movl	%eax, -4(%rbp)
.L7:
	movl	n(%rip), %eax
	cmpl	$995, %eax
	jle	.L8
	movl	-4(%rbp), %eax
	movl	%eax, %esi
	leaq	.LC0(%rip), %rax
	movq	%rax, %rdi
	movl	$0, %eax
	call	printf@PLT
	movl	$0, %eax
	leave
	.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"
	.section	.text.startup,"ax",@progbits
	.p2align 4
	.globl	main
	.type	main, @function
main:
.LFB0:
	.cfi_startproc
	endbr64
	pushq	%r12
	.cfi_def_cfa_offset 16
	.cfi_offset 12, -16
	xorl	%eax, %eax
	movslq	%edi, %r12
	pushq	%rbp
	.cfi_def_cfa_offset 24
	.cfi_offset 6, -24
	leaq	.LC0(%rip), %rbp
	pushq	%rbx
	.cfi_def_cfa_offset 32
	.cfi_offset 3, -32
	leaq	f(%rip), %rbx
	movq	%rbp, %rdi
	movq	%rbx, %rsi
	call	scanf@PLT
	movl	f(%rip), %esi
	testl	%esi, %esi
	je	.L2
	.p2align 4,,10
	.p2align 3
.L7:
	movl	$2, %ecx
	cmpl	$3, %esi
	jle	.L3
	.p2align 4,,10
	.p2align 3
.L6:
	movl	%esi, %eax
	cltd
	idivl	%ecx
	testl	%edx, %edx
	je	.L4
	addl	$1, %ecx
	movl	%ecx, %eax
	imull	%ecx, %eax
	cmpl	%esi, %eax
	jle	.L6
.L3:
	movslq	%esi, %rsi
	addl	$1, (%rbx,%rsi,4)
	movl	(%rbx), %eax
	leal	-1(%rax), %esi
	movl	%esi, (%rbx)
	testl	%esi, %esi
	jne	.L7
	movl	%ecx, k(%rip)
.L2:
	movslq	M(%rip), %rsi
	xorl	%ecx, %ecx
	leaq	8+f(%rip), %rdi
	.p2align 4,,10
	.p2align 3
.L9:
	movl	(%rdi,%rcx,4), %eax
	addq	$1, %rcx
	addl	$1, %eax
	cltq
	imulq	%r12, %rax
	cqto
	idivq	%rsi
	movslq	%edx, %r12
	cmpq	$996, %rcx
	jne	.L9
	movl	%r12d, %esi
	movq	%rbp, %rdi
	xorl	%eax, %eax
	movl	$996, n(%rip)
	call	printf@PLT
	popq	%rbx
	.cfi_remember_state
	.cfi_def_cfa_offset 24
	xorl	%eax, %eax
	popq	%rbp
	.cfi_def_cfa_offset 16
	popq	%r12
	.cfi_def_cfa_offset 8
	ret
	.p2align 4,,10
	.p2align 3
.L4:
	.cfi_restore_state
	movl	%eax, %esi
	movl	%ecx, %eax
	movslq	%ecx, %rdi
	imull	%ecx, %eax
	addl	$1, (%rbx,%rdi,4)
	cmpl	%eax, %esi
	jge	.L6
	jmp	.L3
	.cfi_endproc
.LFE0:
	.size	main, .-main
	.globl	k
	.bss
	.align 4
	.type	k, @object
	.size	k, 4
k:
	.zero	4
	.globl	n
	.align 4
	.type	n, @object
	.size	n, 4
n:
	.zero	4
	.globl	f
	.align 32
	.type	f, @object
	.size	f, 3996
f:
	.zero	3996
	.globl	M
	.data
	.align 4
	.type	M, @object
	.size	M, 4
M:
	.long	1000000007
	.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"
	.section	.text.startup,"ax",@progbits
	.p2align 4
	.globl	main
	.type	main, @function
main:
.LFB0:
	.cfi_startproc
	endbr64
	pushq	%r12
	.cfi_def_cfa_offset 16
	.cfi_offset 12, -16
	xorl	%eax, %eax
	movslq	%edi, %r12
	pushq	%rbp
	.cfi_def_cfa_offset 24
	.cfi_offset 6, -24
	leaq	.LC0(%rip), %rbp
	pushq	%rbx
	.cfi_def_cfa_offset 32
	.cfi_offset 3, -32
	leaq	f(%rip), %rbx
	movq	%rbp, %rdi
	movq	%rbx, %rsi
	call	scanf@PLT
	movl	f(%rip), %esi
	testl	%esi, %esi
	je	.L2
	.p2align 4,,10
	.p2align 3
.L7:
	movl	$2, %ecx
	cmpl	$3, %esi
	jle	.L3
	.p2align 4,,10
	.p2align 3
.L6:
	movl	%esi, %eax
	cltd
	idivl	%ecx
	testl	%edx, %edx
	je	.L4
	addl	$1, %ecx
	movl	%ecx, %eax
	imull	%ecx, %eax
	cmpl	%esi, %eax
	jle	.L6
.L3:
	movslq	%esi, %rsi
	addl	$1, (%rbx,%rsi,4)
	movl	(%rbx), %eax
	leal	-1(%rax), %esi
	movl	%esi, (%rbx)
	testl	%esi, %esi
	jne	.L7
	movl	%ecx, k(%rip)
.L2:
	movslq	M(%rip), %rsi
	xorl	%ecx, %ecx
	leaq	8+f(%rip), %rdi
	.p2align 4,,10
	.p2align 3
.L9:
	movl	(%rdi,%rcx,4), %eax
	addq	$1, %rcx
	addl	$1, %eax
	cltq
	imulq	%r12, %rax
	cqto
	idivq	%rsi
	movslq	%edx, %r12
	cmpq	$996, %rcx
	jne	.L9
	movl	%r12d, %esi
	movq	%rbp, %rdi
	xorl	%eax, %eax
	movl	$996, n(%rip)
	call	printf@PLT
	popq	%rbx
	.cfi_remember_state
	.cfi_def_cfa_offset 24
	xorl	%eax, %eax
	popq	%rbp
	.cfi_def_cfa_offset 16
	popq	%r12
	.cfi_def_cfa_offset 8
	ret
	.p2align 4,,10
	.p2align 3
.L4:
	.cfi_restore_state
	movl	%eax, %esi
	movl	%ecx, %eax
	movslq	%ecx, %rdi
	imull	%ecx, %eax
	addl	$1, (%rbx,%rdi,4)
	cmpl	%eax, %esi
	jge	.L6
	jmp	.L3
	.cfi_endproc
.LFE0:
	.size	main, .-main
	.globl	k
	.bss
	.align 4
	.type	k, @object
	.size	k, 4
k:
	.zero	4
	.globl	n
	.align 4
	.type	n, @object
	.size	n, 4
n:
	.zero	4
	.globl	f
	.align 32
	.type	f, @object
	.size	f, 3996
f:
	.zero	3996
	.globl	M
	.data
	.align 4
	.type	M, @object
	.size	M, 4
M:
	.long	1000000007
	.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:

M=1e9+7;f[999];n;k;main(a){for(scanf("%d",f);n=*f;f[n]++,--*f)for(k=2;k*k<=n;)n%k?k++:(n/=k,f[k]++);for(;n<996;)a=1L*a*-~f[2+n++]%M;printf("%d",a);}
3

4
Given the following C code and unoptimized assembly code, your task is to generate highly optimized x86-64 assembly code.
C Code:

```c
M=1e9+7;f[999];n;k;main(a){for(scanf("%d",f);n=*f;f[n]++,--*f)for(k=2;k*k<=n;)n%k?k++:(n/=k,f[k]++);for(;n<996;)a=1L*a*-~f[2+n++]%M;printf("%d",a);}```

Unoptimized Assembly Code:

```assembly
	.file	"temp.c"
	.text
	.globl	M
	.data
	.align 4
	.type	M, @object
	.size	M, 4
M:
	.long	1000000007
	.globl	f
	.bss
	.align 32
	.type	f, @object
	.size	f, 3996
f:
	.zero	3996
	.globl	n
	.align 4
	.type	n, @object
	.size	n, 4
n:
	.zero	4
	.globl	k
	.align 4
	.type	k, @object
	.size	k, 4
k:
	.zero	4
	.section	.rodata
.LC0:
	.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
	subq	$16, %rsp
	movl	%edi, -4(%rbp)
	leaq	f(%rip), %rax
	movq	%rax, %rsi
	leaq	.LC0(%rip), %rax
	movq	%rax, %rdi
	movl	$0, %eax
	call	scanf@PLT
	jmp	.L2
.L6:
	movl	$2, k(%rip)
	jmp	.L3
.L5:
	movl	n(%rip), %eax
	movl	k(%rip), %ecx
	cltd
	idivl	%ecx
	movl	%edx, %eax
	testl	%eax, %eax
	je	.L4
	movl	k(%rip), %eax
	addl	$1, %eax
	movl	%eax, k(%rip)
	jmp	.L3
.L4:
	movl	n(%rip), %eax
	movl	k(%rip), %esi
	cltd
	idivl	%esi
	movl	%eax, n(%rip)
	movl	k(%rip), %eax
	movslq	%eax, %rdx
	leaq	0(,%rdx,4), %rcx
	leaq	f(%rip), %rdx
	movl	(%rcx,%rdx), %edx
	leal	1(%rdx), %ecx
	cltq
	leaq	0(,%rax,4), %rdx
	leaq	f(%rip), %rax
	movl	%ecx, (%rdx,%rax)
.L3:
	movl	k(%rip), %edx
	movl	k(%rip), %eax
	imull	%eax, %edx
	movl	n(%rip), %eax
	cmpl	%eax, %edx
	jle	.L5
	movl	n(%rip), %eax
	movslq	%eax, %rdx
	leaq	0(,%rdx,4), %rcx
	leaq	f(%rip), %rdx
	movl	(%rcx,%rdx), %edx
	leal	1(%rdx), %ecx
	cltq
	leaq	0(,%rax,4), %rdx
	leaq	f(%rip), %rax
	movl	%ecx, (%rdx,%rax)
	movl	f(%rip), %eax
	subl	$1, %eax
	movl	%eax, f(%rip)
.L2:
	movl	f(%rip), %eax
	movl	%eax, n(%rip)
	movl	n(%rip), %eax
	testl	%eax, %eax
	jne	.L6
	jmp	.L7
.L8:
	movl	-4(%rbp), %eax
	movslq	%eax, %rcx
	movl	n(%rip), %eax
	leal	1(%rax), %edx
	movl	%edx, n(%rip)
	addl	$2, %eax
	cltq
	leaq	0(,%rax,4), %rdx
	leaq	f(%rip), %rax
	movl	(%rdx,%rax), %eax
	addl	$1, %eax
	cltq
	imulq	%rcx, %rax
	movl	M(%rip), %edx
	movslq	%edx, %rcx
	cqto
	idivq	%rcx
	movq	%rdx, %rax
	movl	%eax, -4(%rbp)
.L7:
	movl	n(%rip), %eax
	cmpl	$995, %eax
	jle	.L8
	movl	-4(%rbp), %eax
	movl	%eax, %esi
	leaq	.LC0(%rip), %rax
	movq	%rax, %rdi
	movl	$0, %eax
	call	printf@PLT
	movl	$0, %eax
	leave
	.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.
val
	.file	"temp.c"
	.text
	.globl	M
	.data
	.align 4
	.type	M, @object
	.size	M, 4
M:
	.long	1000000007
	.globl	f
	.bss
	.align 32
	.type	f, @object
	.size	f, 3996
f:
	.zero	3996
	.globl	n
	.align 4
	.type	n, @object
	.size	n, 4
n:
	.zero	4
	.globl	k
	.align 4
	.type	k, @object
	.size	k, 4
k:
	.zero	4
	.section	.rodata
.LC0:
	.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
	subq	$16, %rsp
	movl	%edi, -4(%rbp)
	leaq	f(%rip), %rax
	movq	%rax, %rsi
	leaq	.LC0(%rip), %rax
	movq	%rax, %rdi
	movl	$0, %eax
	call	scanf@PLT
	jmp	.L2
.L6:
	movl	$2, k(%rip)
	jmp	.L3
.L5:
	movl	n(%rip), %eax
	movl	k(%rip), %ecx
	cltd
	idivl	%ecx
	movl	%edx, %eax
	testl	%eax, %eax
	je	.L4
	movl	k(%rip), %eax
	addl	$1, %eax
	movl	%eax, k(%rip)
	jmp	.L3
.L4:
	movl	n(%rip), %eax
	movl	k(%rip), %esi
	cltd
	idivl	%esi
	movl	%eax, n(%rip)
	movl	k(%rip), %eax
	movslq	%eax, %rdx
	leaq	0(,%rdx,4), %rcx
	leaq	f(%rip), %rdx
	movl	(%rcx,%rdx), %edx
	leal	1(%rdx), %ecx
	cltq
	leaq	0(,%rax,4), %rdx
	leaq	f(%rip), %rax
	movl	%ecx, (%rdx,%rax)
.L3:
	movl	k(%rip), %edx
	movl	k(%rip), %eax
	imull	%eax, %edx
	movl	n(%rip), %eax
	cmpl	%eax, %edx
	jle	.L5
	movl	n(%rip), %eax
	movslq	%eax, %rdx
	leaq	0(,%rdx,4), %rcx
	leaq	f(%rip), %rdx
	movl	(%rcx,%rdx), %edx
	leal	1(%rdx), %ecx
	cltq
	leaq	0(,%rax,4), %rdx
	leaq	f(%rip), %rax
	movl	%ecx, (%rdx,%rax)
	movl	f(%rip), %eax
	subl	$1, %eax
	movl	%eax, f(%rip)
.L2:
	movl	f(%rip), %eax
	movl	%eax, n(%rip)
	movl	n(%rip), %eax
	testl	%eax, %eax
	jne	.L6
	jmp	.L7
.L8:
	movl	-4(%rbp), %eax
	movslq	%eax, %rcx
	movl	n(%rip), %eax
	leal	1(%rax), %edx
	movl	%edx, n(%rip)
	addl	$2, %eax
	cltq
	leaq	0(,%rax,4), %rdx
	leaq	f(%rip), %rax
	movl	(%rdx,%rax), %eax
	addl	$1, %eax
	cltq
	imulq	%rcx, %rax
	movl	M(%rip), %edx
	movslq	%edx, %rcx
	cqto
	idivq	%rcx
	movq	%rdx, %rax
	movl	%eax, -4(%rbp)
.L7:
	movl	n(%rip), %eax
	cmpl	$995, %eax
	jle	.L8
	movl	-4(%rbp), %eax
	movl	%eax, %esi
	leaq	.LC0(%rip), %rax
	movq	%rax, %rdi
	movl	$0, %eax
	call	printf@PLT
	movl	$0, %eax
	leave
	.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:
