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

```c
#include <stdio.h>
#include <stdlib.h>
#include <math.h>
#define M 1000000007
int factor(int n,int i){
    int ans=0,temp=i;
    //printf("i=%d",i);
    while(n/i!=0){
        //printf(" n/i=%d",n/i);
        ans+=n/i;
        i*=temp;
    }
    //printf(" ans=%d\n",ans);
    return ans;
}
int main(void){
    int n;
    scanf("%d",&n);
    int i,j,flag;
    long long int ans=1;
    for(i=2;i<=n;i++){
        flag=1;
        for(j=2;j<=sqrt(i);j++){
            if(i%j==0){
                flag=0;
                break;}
            }
            //素数であれば
            if(flag==1){
                ans=(ans*(factor(n,i)+1))%M;
            }
        }
    printf("%lld\n",ans);
}

```

Assembly Code:

```assembly
	.file	"temp.c"
	.text
	.p2align 4
	.globl	factor
	.type	factor, @function
factor:
.LFB39:
	.cfi_startproc
	endbr64
	movl	%edi, %eax
	cltd
	idivl	%esi
	testl	%eax, %eax
	je	.L4
	movl	%esi, %ecx
	xorl	%r8d, %r8d
	.p2align 4,,10
	.p2align 3
.L3:
	imull	%esi, %ecx
	addl	%eax, %r8d
	movl	%edi, %eax
	cltd
	idivl	%ecx
	testl	%eax, %eax
	jne	.L3
	movl	%r8d, %eax
	ret
	.p2align 4,,10
	.p2align 3
.L4:
	xorl	%r8d, %r8d
	movl	%r8d, %eax
	ret
	.cfi_endproc
.LFE39:
	.size	factor, .-factor
	.section	.rodata.str1.1,"aMS",@progbits,1
.LC0:
	.string	"%d"
.LC2:
	.string	"%lld\n"
	.section	.text.startup,"ax",@progbits
	.p2align 4
	.globl	main
	.type	main, @function
main:
.LFB40:
	.cfi_startproc
	endbr64
	pushq	%r15
	.cfi_def_cfa_offset 16
	.cfi_offset 15, -16
	leaq	.LC0(%rip), %rdi
	pushq	%r14
	.cfi_def_cfa_offset 24
	.cfi_offset 14, -24
	pushq	%r13
	.cfi_def_cfa_offset 32
	.cfi_offset 13, -32
	pushq	%r12
	.cfi_def_cfa_offset 40
	.cfi_offset 12, -40
	pushq	%rbp
	.cfi_def_cfa_offset 48
	.cfi_offset 6, -48
	pushq	%rbx
	.cfi_def_cfa_offset 56
	.cfi_offset 3, -56
	subq	$40, %rsp
	.cfi_def_cfa_offset 96
	movq	%fs:40, %rax
	movq	%rax, 24(%rsp)
	xorl	%eax, %eax
	leaq	20(%rsp), %rsi
	call	__isoc99_scanf@PLT
	movl	20(%rsp), %ebp
	cmpl	$1, %ebp
	jle	.L22
	leal	1(%rbp), %r13d
	movl	$1, %r12d
	movl	$2, %ebx
	movabsq	$-8543223828751151131, %r14
	pxor	%xmm2, %xmm2
	.p2align 4,,10
	.p2align 3
.L9:
	pxor	%xmm1, %xmm1
	cvtsi2sdl	%ebx, %xmm1
	ucomisd	%xmm1, %xmm2
	ja	.L31
	sqrtsd	%xmm1, %xmm1
	movl	$2, %ecx
	jmp	.L17
	.p2align 4,,10
	.p2align 3
.L12:
	movl	%ebx, %eax
	cltd
	idivl	%ecx
	testl	%edx, %edx
	je	.L11
	addl	$1, %ecx
.L17:
	pxor	%xmm0, %xmm0
	cvtsi2sdl	%ecx, %xmm0
	comisd	%xmm0, %xmm1
	jnb	.L12
.L18:
	movl	%ebp, %eax
	cltd
	idivl	%ebx
	testl	%eax, %eax
	je	.L23
	movl	%ebx, %ecx
	xorl	%esi, %esi
.L14:
	imull	%ebx, %ecx
	addl	%eax, %esi
	movl	%ebp, %eax
	cltd
	idivl	%ecx
	testl	%eax, %eax
	jne	.L14
.L13:
	addl	$1, %esi
	movslq	%esi, %rsi
	imulq	%r12, %rsi
	movq	%rsi, %rax
	mulq	%r14
	shrq	$29, %rdx
	imulq	$1000000007, %rdx, %rax
	subq	%rax, %rsi
	movq	%rsi, %r12
.L11:
	addl	$1, %ebx
	cmpl	%ebx, %r13d
	jne	.L9
.L8:
	xorl	%eax, %eax
	movq	%r12, %rdx
	movl	$1, %edi
	leaq	.LC2(%rip), %rsi
	call	__printf_chk@PLT
	movq	24(%rsp), %rax
	subq	%fs:40, %rax
	jne	.L33
	addq	$40, %rsp
	.cfi_remember_state
	.cfi_def_cfa_offset 56
	xorl	%eax, %eax
	popq	%rbx
	.cfi_def_cfa_offset 48
	popq	%rbp
	.cfi_def_cfa_offset 40
	popq	%r12
	.cfi_def_cfa_offset 32
	popq	%r13
	.cfi_def_cfa_offset 24
	popq	%r14
	.cfi_def_cfa_offset 16
	popq	%r15
	.cfi_def_cfa_offset 8
	ret
.L23:
	.cfi_restore_state
	xorl	%esi, %esi
	jmp	.L13
.L22:
	movl	$1, %r12d
	jmp	.L8
.L31:
	movl	$2, %r15d
	jmp	.L15
.L34:
	movl	%ebx, %eax
	cltd
	idivl	%r15d
	testl	%edx, %edx
	je	.L11
	movsd	8(%rsp), %xmm1
	addl	$1, %r15d
.L15:
	movapd	%xmm1, %xmm0
	movsd	%xmm1, 8(%rsp)
	call	sqrt@PLT
	pxor	%xmm2, %xmm2
	movapd	%xmm0, %xmm3
	pxor	%xmm0, %xmm0
	cvtsi2sdl	%r15d, %xmm0
	comisd	%xmm0, %xmm3
	jnb	.L34
	jmp	.L18
.L33:
	call	__stack_chk_fail@PLT
	.cfi_endproc
.LFE40:
	.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.
Optimized Assembly Code:

user
```assembly
	.file	"temp.c"
	.text
	.p2align 4
	.globl	factor
	.type	factor, @function
factor:
.LFB39:
	.cfi_startproc
	endbr64
	movl	%edi, %eax
	cltd
	idivl	%esi
	testl	%eax, %eax
	je	.L4
	movl	%esi, %ecx
	xorl	%r8d, %r8d
	.p2align 4,,10
	.p2align 3
.L3:
	imull	%esi, %ecx
	addl	%eax, %r8d
	movl	%edi, %eax
	cltd
	idivl	%ecx
	testl	%eax, %eax
	jne	.L3
	movl	%r8d, %eax
	ret
	.p2align 4,,10
	.p2align 3
.L4:
	xorl	%r8d, %r8d
	movl	%r8d, %eax
	ret
	.cfi_endproc
.LFE39:
	.size	factor, .-factor
	.section	.rodata.str1.1,"aMS",@progbits,1
.LC0:
	.string	"%d"
.LC2:
	.string	"%lld\n"
	.section	.text.startup,"ax",@progbits
	.p2align 4
	.globl	main
	.type	main, @function
main:
.LFB40:
	.cfi_startproc
	endbr64
	pushq	%r15
	.cfi_def_cfa_offset 16
	.cfi_offset 15, -16
	leaq	.LC0(%rip), %rdi
	pushq	%r14
	.cfi_def_cfa_offset 24
	.cfi_offset 14, -24
	pushq	%r13
	.cfi_def_cfa_offset 32
	.cfi_offset 13, -32
	pushq	%r12
	.cfi_def_cfa_offset 40
	.cfi_offset 12, -40
	pushq	%rbp
	.cfi_def_cfa_offset 48
	.cfi_offset 6, -48
	pushq	%rbx
	.cfi_def_cfa_offset 56
	.cfi_offset 3, -56
	subq	$40, %rsp
	.cfi_def_cfa_offset 96
	movq	%fs:40, %rax
	movq	%rax, 24(%rsp)
	xorl	%eax, %eax
	leaq	20(%rsp), %rsi
	call	__isoc99_scanf@PLT
	movl	20(%rsp), %ebp
	cmpl	$1, %ebp
	jle	.L22
	leal	1(%rbp), %r13d
	movl	$1, %r12d
	movl	$2, %ebx
	movabsq	$-8543223828751151131, %r14
	pxor	%xmm2, %xmm2
	.p2align 4,,10
	.p2align 3
.L9:
	pxor	%xmm1, %xmm1
	cvtsi2sdl	%ebx, %xmm1
	ucomisd	%xmm1, %xmm2
	ja	.L31
	sqrtsd	%xmm1, %xmm1
	movl	$2, %ecx
	jmp	.L17
	.p2align 4,,10
	.p2align 3
.L12:
	movl	%ebx, %eax
	cltd
	idivl	%ecx
	testl	%edx, %edx
	je	.L11
	addl	$1, %ecx
.L17:
	pxor	%xmm0, %xmm0
	cvtsi2sdl	%ecx, %xmm0
	comisd	%xmm0, %xmm1
	jnb	.L12
.L18:
	movl	%ebp, %eax
	cltd
	idivl	%ebx
	testl	%eax, %eax
	je	.L23
	movl	%ebx, %ecx
	xorl	%esi, %esi
.L14:
	imull	%ebx, %ecx
	addl	%eax, %esi
	movl	%ebp, %eax
	cltd
	idivl	%ecx
	testl	%eax, %eax
	jne	.L14
.L13:
	addl	$1, %esi
	movslq	%esi, %rsi
	imulq	%r12, %rsi
	movq	%rsi, %rax
	mulq	%r14
	shrq	$29, %rdx
	imulq	$1000000007, %rdx, %rax
	subq	%rax, %rsi
	movq	%rsi, %r12
.L11:
	addl	$1, %ebx
	cmpl	%ebx, %r13d
	jne	.L9
.L8:
	xorl	%eax, %eax
	movq	%r12, %rdx
	movl	$1, %edi
	leaq	.LC2(%rip), %rsi
	call	__printf_chk@PLT
	movq	24(%rsp), %rax
	subq	%fs:40, %rax
	jne	.L33
	addq	$40, %rsp
	.cfi_remember_state
	.cfi_def_cfa_offset 56
	xorl	%eax, %eax
	popq	%rbx
	.cfi_def_cfa_offset 48
	popq	%rbp
	.cfi_def_cfa_offset 40
	popq	%r12
	.cfi_def_cfa_offset 32
	popq	%r13
	.cfi_def_cfa_offset 24
	popq	%r14
	.cfi_def_cfa_offset 16
	popq	%r15
	.cfi_def_cfa_offset 8
	ret
.L23:
	.cfi_restore_state
	xorl	%esi, %esi
	jmp	.L13
.L22:
	movl	$1, %r12d
	jmp	.L8
.L31:
	movl	$2, %r15d
	jmp	.L15
.L34:
	movl	%ebx, %eax
	cltd
	idivl	%r15d
	testl	%edx, %edx
	je	.L11
	movsd	8(%rsp), %xmm1
	addl	$1, %r15d
.L15:
	movapd	%xmm1, %xmm0
	movsd	%xmm1, 8(%rsp)
	call	sqrt@PLT
	pxor	%xmm2, %xmm2
	movapd	%xmm0, %xmm3
	pxor	%xmm0, %xmm0
	cvtsi2sdl	%r15d, %xmm0
	comisd	%xmm0, %xmm3
	jnb	.L34
	jmp	.L18
.L33:
	call	__stack_chk_fail@PLT
	.cfi_endproc
.LFE40:
	.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
```assembly
	.file	"temp.c"
	.text
	.p2align 4
	.globl	factor
	.type	factor, @function
factor:
.LFB39:
	.cfi_startproc
	endbr64
	movl	%edi, %eax
	cltd
	idivl	%esi
	testl	%eax, %eax
	je	.L4
	movl	%esi, %ecx
	xorl	%r8d, %r8d
	.p2align 4,,10
	.p2align 3
.L3:
	imull	%esi, %ecx
	addl	%eax, %r8d
	movl	%edi, %eax
	cltd
	idivl	%ecx
	testl	%eax, %eax
	jne	.L3
	movl	%r8d, %eax
	ret
	.p2align 4,,10
	.p2align 3
.L4:
	xorl	%r8d, %r8d
	movl	%r8d, %eax
	ret
	.cfi_endproc
.LFE39:
	.size	factor, .-factor
	.section	.rodata.str1.1,"aMS",@progbits,1
.LC0:
	.string	"%d"
.LC2:
	.string	"%lld\n"
	.section	.text.startup,"ax",@progbits
	.p2align 4
	.globl	main
	.type	main, @function
main:
.LFB40:
	.cfi_startproc
	endbr64
	pushq	%r15
	.cfi_def_cfa_offset 16
	.cfi_offset 15, -16
	leaq	.LC0(%rip), %rdi
	pushq	%r14
	.cfi_def_cfa_offset 24
	.cfi_offset 14, -24
	pushq	%r13
	.cfi_def_cfa_offset 32
	.cfi_offset 13, -32
	pushq	%r12
	.cfi_def_cfa_offset 40
	.cfi_offset 12, -40
	pushq	%rbp
	.cfi_def_cfa_offset 48
	.cfi_offset 6, -48
	pushq	%rbx
	.cfi_def_cfa_offset 56
	.cfi_offset 3, -56
	subq	$40, %rsp
	.cfi_def_cfa_offset 96
	movq	%fs:40, %rax
	movq	%rax, 24(%rsp)
	xorl	%eax, %eax
	leaq	20(%rsp), %rsi
	call	__isoc99_scanf@PLT
	movl	20(%rsp), %ebp
	cmpl	$1, %ebp
	jle	.L22
	leal	1(%rbp), %r13d
	movl	$1, %r12d
	movl	$2, %ebx
	movabsq	$-8543223828751151131, %r14
	pxor	%xmm2, %xmm2
	.p2align 4,,10
	.p2align 3
.L9:
	pxor	%xmm1, %xmm1
	cvtsi2sdl	%ebx, %xmm1
	ucomisd	%xmm1, %xmm2
	ja	.L31
	sqrtsd	%xmm1, %xmm1
	movl	$2, %ecx
	jmp	.L17
	.p2align 4,,10
	.p2align 3
.L12:
	movl	%ebx, %eax
	cltd
	idivl	%ecx
	testl	%edx, %edx
	je	.L11
	addl	$1, %ecx
.L17:
	pxor	%xmm0, %xmm0
	cvtsi2sdl	%ecx, %xmm0
	comisd	%xmm0, %xmm1
	jnb	.L12
.L18:
	movl	%ebp, %eax
	cltd
	idivl	%ebx
	testl	%eax, %eax
	je	.L23
	movl	%ebx, %ecx
	xorl	%esi, %esi
.L14:
	imull	%ebx, %ecx
	addl	%eax, %esi
	movl	%ebp, %eax
	cltd
	idivl	%ecx
	testl	%eax, %eax
	jne	.L14
.L13:
	addl	$1, %esi
	movslq	%esi, %rsi
	imulq	%r12, %rsi
	movq	%rsi, %rax
	mulq	%r14
	shrq	$29, %rdx
	imulq	$1000000007, %rdx, %rax
	subq	%rax, %rsi
	movq	%rsi, %r12
.L11:
	addl	$1, %ebx
	cmpl	%ebx, %r13d
	jne	.L9
.L8:
	xorl	%eax, %eax
	movq	%r12, %rdx
	movl	$1, %edi
	leaq	.LC2(%rip), %rsi
	call	__printf_chk@PLT
	movq	24(%rsp), %rax
	subq	%fs:40, %rax
	jne	.L33
	addq	$40, %rsp
	.cfi_remember_state
	.cfi_def_cfa_offset 56
	xorl	%eax, %eax
	popq	%rbx
	.cfi_def_cfa_offset 48
	popq	%rbp
	.cfi_def_cfa_offset 40
	popq	%r12
	.cfi_def_cfa_offset 32
	popq	%r13
	.cfi_def_cfa_offset 24
	popq	%r14
	.cfi_def_cfa_offset 16
	popq	%r15
	.cfi_def_cfa_offset 8
	ret
.L23:
	.cfi_restore_state
	xorl	%esi, %esi
	jmp	.L13
.L22:
	movl	$1, %r12d
	jmp	.L8
.L31:
	movl	$2, %r15d
	jmp	.L15
.L34:
	movl	%ebx, %eax
	cltd
	idivl	%r15d
	testl	%edx, %edx
	je	.L11
	movsd	8(%rsp), %xmm1
	addl	$1, %r15d
.L15:
	movapd	%xmm1, %xmm0
	movsd	%xmm1, 8(%rsp)
	call	sqrt@PLT
	pxor	%xmm2, %xmm2
	movapd	%xmm0, %xmm3
	pxor	%xmm0, %xmm0
	cvtsi2sdl	%r15d, %xmm0
	comisd	%xmm0, %xmm3
	jnb	.L34
	jmp	.L18
.L33:
	call	__stack_chk_fail@PLT
	.cfi_endproc
.LFE40:
	.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:
```
```c
#include <stdio.h>
#include <stdlib.h>
#include <math.h>
#define M 1000000007
int factor(int n,int i){
    int ans=0,temp=i;
    //printf("i=%d",i);
    while(n/i!=0){
        //printf(" n/i=%d",n/i);
        ans+=n/i;
        i*=temp;
    }
    //printf(" ans=%d\n",ans);
    return ans;
}
int main(void){
    int n;
    scanf("%d",&n);
    int i,j,flag;
    long long int ans=1;
    for(i=2;i<=n;i++){
        flag=1;
        for(j=2;j<=sqrt(i);j++){
            if(i%j==0){
                flag=0;
                break;}
            }
            //素数であれば
            if(flag==1){
                ans=(ans*(factor(n,i)+1))%M;
            }
        }
    printf("%lld\n",ans);
}

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

```c
#include <stdio.h>
#include <stdlib.h>
#include <math.h>
#define M 1000000007
int factor(int n,int i){
    int ans=0,temp=i;
    //printf("i=%d",i);
    while(n/i!=0){
        //printf(" n/i=%d",n/i);
        ans+=n/i;
        i*=temp;
    }
    //printf(" ans=%d\n",ans);
    return ans;
}
int main(void){
    int n;
    scanf("%d",&n);
    int i,j,flag;
    long long int ans=1;
    for(i=2;i<=n;i++){
        flag=1;
        for(j=2;j<=sqrt(i);j++){
            if(i%j==0){
                flag=0;
                break;}
            }
            //素数であれば
            if(flag==1){
                ans=(ans*(factor(n,i)+1))%M;
            }
        }
    printf("%lld\n",ans);
}

```

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.
Optimized Assembly Code:

3

4

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

```c
#include <stdio.h>
#include <stdlib.h>
#include <math.h>
#define M 1000000007
int factor(int n,int i){
    int ans=0,temp=i;
    //printf("i=%d",i);
    while(n/i!=0){
        //printf(" n/i=%d",n/i);
        ans+=n/i;
        i*=temp;
    }
    //printf(" ans=%d\n",ans);
    return ans;
}
int main(void){
    int n;
    scanf("%d",&n);
    int i,j,flag;
    long long int ans=1;
    for(i=2;i<=n;i++){
        flag=1;
        for(j=2;j<=sqrt(i);j++){
            if(i%j==0){
                flag=0;
                break;}
            }
            //素数であれば
            if(flag==1){
                ans=(ans*(factor(n,i)+1))%M;
            }
        }
    printf("%lld\n",ans);
}

```

Assembly Code:

```assembly
	.file	"temp.c"
	.text
	.p2align 4
	.globl	factor
	.type	factor, @function
factor:
.LFB39:
	.cfi_startproc
	endbr64
	movl	%edi, %eax
	cltd
	idivl	%esi
	testl	%eax, %eax
	je	.L4
	movl	%esi, %ecx
	xorl	%r8d, %r8d
	.p2align 4,,10
	.p2align 3
.L3:
	imull	%esi, %ecx
	addl	%eax, %r8d
	movl	%edi, %eax
	cltd
	idivl	%ecx
	testl	%eax, %eax
	jne	.L3
	movl	%r8d, %eax
	ret
	.p2align 4,,10
	.p2align 3
.L4:
	xorl	%r8d, %r8d
	movl	%r8d, %eax
	ret
	.cfi_endproc
.LFE39:
	.size	factor, .-factor
	.section	.rodata.str1.1,"aMS",@progbits,1
.LC0:
	.string	"%d"
.LC2:
	.string	"%lld\n"
	.section	.text.startup,"ax",@progbits
	.p2align 4
	.globl	main
	.type	main, @function
main:
.LFB40:
	.cfi_startproc
	endbr64
	pushq	%r15
	.cfi_def_cfa_offset 16
	.cfi_offset 15, -16
	leaq	.LC0(%rip), %rdi
	pushq	%r14
	.cfi_def_cfa_offset 24
	.cfi_offset 14, -24
	pushq	%r13
	.cfi_def_cfa_offset 32
	.cfi_offset 13, -32
	pushq	%r12
	.cfi_def_cfa_offset 40
	.cfi_offset 12, -40
	pushq	%rbp
	.cfi_def_cfa_offset 48
	.cfi_offset 6, -48
	pushq	%rbx
	.cfi_def_cfa_offset 56
	.cfi_offset 3, -56
	subq	$40, %rsp
	.cfi_def_cfa_offset 96
	movq	%fs:40, %rax
	movq	%rax, 24(%rsp)
	xorl	%eax, %eax
	leaq	20(%rsp), %rsi
	call	__isoc99_scanf@PLT
	movl	20(%rsp), %ebp
	cmpl	$1, %ebp
	jle	.L22
	leal	1(%rbp), %r13d
	movl	$1, %r12d
	movl	$2, %ebx
	movabsq	$-8543223828751151131, %r14
	pxor	%xmm2, %xmm2
	.p2align 4,,10
	.p2align 3
.L9:
	pxor	%xmm1, %xmm1
	cvtsi2sdl	%ebx, %xmm1
	ucomisd	%xmm1, %xmm2
	ja	.L31
	sqrtsd	%xmm1, %xmm1
	movl	$2, %ecx
	jmp	.L17
	.p2align 4,,10
	.p2align 3
.L12:
	movl	%ebx, %eax
	cltd
	idivl	%ecx
	testl	%edx, %edx
	je	.L11
	addl	$1, %ecx
.L17:
	pxor	%xmm0, %xmm0
	cvtsi2sdl	%ecx, %xmm0
	comisd	%xmm0, %xmm1
	jnb	.L12
.L18:
	movl	%ebp, %eax
	cltd
	idivl	%ebx
	testl	%eax, %eax
	je	.L23
	movl	%ebx, %ecx
	xorl	%esi, %esi
.L14:
	imull	%ebx, %ecx
	addl	%eax, %esi
	movl	%ebp, %eax
	cltd
	idivl	%ecx
	testl	%eax, %eax
	jne	.L14
.L13:
	addl	$1, %esi
	movslq	%esi, %rsi
	imulq	%r12, %rsi
	movq	%rsi, %rax
	mulq	%r14
	shrq	$29, %rdx
	imulq	$1000000007, %rdx, %rax
	subq	%rax, %rsi
	movq	%rsi, %r12
.L11:
	addl	$1, %ebx
	cmpl	%ebx, %r13d
	jne	.L9
.L8:
	xorl	%eax, %eax
	movq	%r12, %rdx
	movl	$1, %edi
	leaq	.LC2(%rip), %rsi
	call	__printf_chk@PLT
	movq	24(%rsp), %rax
	subq	%fs:40, %rax
	jne	.L33
	addq	$40, %rsp
	.cfi_remember_state
	.cfi_def_cfa_offset 56
	xorl	%eax, %eax
	popq	%rbx
	.cfi_def_cfa_offset 48
	popq	%rbp
	.cfi_def_cfa_offset 40
	popq	%r12
	.cfi_def_cfa_offset 32
	popq	%r13
	.cfi_def_cfa_offset 24
	popq	%r14
	.cfi_def_cfa_offset 16
	popq	%r15
	.cfi_def_cfa_offset 8
	ret
.L23:
	.cfi_restore_state
	xorl	%esi, %esi
	jmp	.L13
.L22:
	movl	$1, %r12d
	jmp	.L8
.L31:
	movl	$2, %r15d
	jmp	.L15
.L34:
	movl	%ebx, %eax
	cltd
	idivl	%r15d
	testl	%edx, %edx
	je	.L11
	movsd	8(%rsp), %xmm1
	addl	$1, %r15d
.L15:
	movapd	%xmm1, %xmm0
	movsd	%xmm1, 8(%rsp)
	call	sqrt@PLT
	pxor	%xmm2, %xmm2
	movapd	%xmm0, %xmm3
	pxor	%xmm0, %xmm0
	cvtsi2sdl	%r15d, %xmm0
	comisd	%xmm0, %xmm3
	jnb	.L34
	jmp	.L18
.L33:
	call	__stack_chk_fail@PLT
	.cfi_endproc
.LFE40:
	.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.
Optimized Assembly Code:

train
```assembly
	.file	"temp.c"
	.text
	.p2align 4
	.globl	factor
	.type	factor, @function
factor:
.LFB39:
	.cfi_startproc
	endbr64
	movl	%edi, %eax
	cltd
	idivl	%esi
	testl	%eax, %eax
	je	.L4
	movl	%esi, %ecx
	xorl	%r8d, %r8d
	.p2align 4,,10
	.p2align 3
.L3:
	imull	%esi, %ecx
	addl	%eax, %r8d
	movl	%edi, %eax
	cltd
	idivl	%ecx
	testl	%eax, %eax
	jne	.L3
	movl	%r8d, %eax
	ret
	.p2align 4,,10
	.p2align 3
.L4:
	xorl	%r8d, %r8d
	movl	%r8d, %eax
	ret
	.cfi_endproc
.LFE39:
	.size	factor, .-factor
	.section	.rodata.str1.1,"aMS",@progbits,1
.LC0:
	.string	"%d"
.LC2:
	.string	"%lld\n"
	.section	.text.startup,"ax",@progbits
	.p2align 4
	.globl	main
	.type	main, @function
main:
.LFB40:
	.cfi_startproc
	endbr64
	pushq	%r15
	.cfi_def_cfa_offset 16
	.cfi_offset 15, -16
	leaq	.LC0(%rip), %rdi
	pushq	%r14
	.cfi_def_cfa_offset 24
	.cfi_offset 14, -24
	pushq	%r13
	.cfi_def_cfa_offset 32
	.cfi_offset 13, -32
	pushq	%r12
	.cfi_def_cfa_offset 40
	.cfi_offset 12, -40
	pushq	%rbp
	.cfi_def_cfa_offset 48
	.cfi_offset 6, -48
	pushq	%rbx
	.cfi_def_cfa_offset 56
	.cfi_offset 3, -56
	subq	$40, %rsp
	.cfi_def_cfa_offset 96
	movq	%fs:40, %rax
	movq	%rax, 24(%rsp)
	xorl	%eax, %eax
	leaq	20(%rsp), %rsi
	call	__isoc99_scanf@PLT
	movl	20(%rsp), %ebp
	cmpl	$1, %ebp
	jle	.L22
	leal	1(%rbp), %r13d
	movl	$1, %r12d
	movl	$2, %ebx
	movabsq	$-8543223828751151131, %r14
	pxor	%xmm2, %xmm2
	.p2align 4,,10
	.p2align 3
.L9:
	pxor	%xmm1, %xmm1
	cvtsi2sdl	%ebx, %xmm1
	ucomisd	%xmm1, %xmm2
	ja	.L31
	sqrtsd	%xmm1, %xmm1
	movl	$2, %ecx
	jmp	.L17
	.p2align 4,,10
	.p2align 3
.L12:
	movl	%ebx, %eax
	cltd
	idivl	%ecx
	testl	%edx, %edx
	je	.L11
	addl	$1, %ecx
.L17:
	pxor	%xmm0, %xmm0
	cvtsi2sdl	%ecx, %xmm0
	comisd	%xmm0, %xmm1
	jnb	.L12
.L18:
	movl	%ebp, %eax
	cltd
	idivl	%ebx
	testl	%eax, %eax
	je	.L23
	movl	%ebx, %ecx
	xorl	%esi, %esi
.L14:
	imull	%ebx, %ecx
	addl	%eax, %esi
	movl	%ebp, %eax
	cltd
	idivl	%ecx
	testl	%eax, %eax
	jne	.L14
.L13:
	addl	$1, %esi
	movslq	%esi, %rsi
	imulq	%r12, %rsi
	movq	%rsi, %rax
	mulq	%r14
	shrq	$29, %rdx
	imulq	$1000000007, %rdx, %rax
	subq	%rax, %rsi
	movq	%rsi, %r12
.L11:
	addl	$1, %ebx
	cmpl	%ebx, %r13d
	jne	.L9
.L8:
	xorl	%eax, %eax
	movq	%r12, %rdx
	movl	$1, %edi
	leaq	.LC2(%rip), %rsi
	call	__printf_chk@PLT
	movq	24(%rsp), %rax
	subq	%fs:40, %rax
	jne	.L33
	addq	$40, %rsp
	.cfi_remember_state
	.cfi_def_cfa_offset 56
	xorl	%eax, %eax
	popq	%rbx
	.cfi_def_cfa_offset 48
	popq	%rbp
	.cfi_def_cfa_offset 40
	popq	%r12
	.cfi_def_cfa_offset 32
	popq	%r13
	.cfi_def_cfa_offset 24
	popq	%r14
	.cfi_def_cfa_offset 16
	popq	%r15
	.cfi_def_cfa_offset 8
	ret
.L23:
	.cfi_restore_state
	xorl	%esi, %esi
	jmp	.L13
.L22:
	movl	$1, %r12d
	jmp	.L8
.L31:
	movl	$2, %r15d
	jmp	.L15
.L34:
	movl	%ebx, %eax
	cltd
	idivl	%r15d
	testl	%edx, %edx
	je	.L11
	movsd	8(%rsp), %xmm1
	addl	$1, %r15d
.L15:
	movapd	%xmm1, %xmm0
	movsd	%xmm1, 8(%rsp)
	call	sqrt@PLT
	pxor	%xmm2, %xmm2
	movapd	%xmm0, %xmm3
	pxor	%xmm0, %xmm0
	cvtsi2sdl	%r15d, %xmm0
	comisd	%xmm0, %xmm3
	jnb	.L34
	jmp	.L18
.L33:
	call	__stack_chk_fail@PLT
	.cfi_endproc
.LFE40:
	.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:
```