; LLVM IR from ShahjalalShohag/code-library :: Number Theory (Derangement)

; Unoptimized IR (clang -disable-llvm-passes):
target datalayout = "e-m:e-p270:32:32-p271:32:32-p272:64:64-i64:64-i128:128-f80:128-n8:16:32:64-S128"
target triple = "x86_64-unknown-linux-gnu"

%"class.std::basic_istream" = type { ptr, i64, %"class.std::basic_ios" }
%"class.std::basic_ios" = type { %"class.std::ios_base", ptr, i8, i8, ptr, ptr, ptr, ptr }
%"class.std::ios_base" = type { ptr, i64, i64, i32, i32, i32, ptr, %"struct.std::ios_base::_Words", [8 x %"struct.std::ios_base::_Words"], i32, ptr, %"class.std::locale" }
%"struct.std::ios_base::_Words" = type { ptr, i64 }
%"class.std::locale" = type { ptr }
%"class.std::basic_ostream" = type { ptr, %"class.std::basic_ios" }

@d = external dso_local global [1000009 x i32], align 16
@_ZSt3cin = external global %"class.std::basic_istream", align 8
@_ZSt4cout = external global %"class.std::basic_ostream", align 8

; Function Attrs: mustprogress norecurse uwtable
define dso_local noundef i32 @main() #0 {
  %1 = alloca i32, align 4
  %2 = alloca i32, align 4
  %3 = alloca i32, align 4
  store i32 0, ptr %1, align 4
  %4 = call noundef zeroext i1 @_ZNSt8ios_base15sync_with_stdioEb(i1 noundef zeroext false)
  %5 = load ptr, ptr @_ZSt3cin, align 8, !tbaa !5
  %6 = getelementptr i8, ptr %5, i64 -24
  %7 = load i64, ptr %6, align 8
  %8 = getelementptr inbounds i8, ptr @_ZSt3cin, i64 %7
  %9 = call noundef ptr @_ZNSt9basic_iosIcSt11char_traitsIcEE3tieEPSo(ptr noundef nonnull align 8 dereferenceable(264) %8, ptr noundef null)
  store i32 1, ptr @d, align 16, !tbaa !8
  store i32 0, ptr getelementptr inbounds ([1000009 x i32], ptr @d, i64 0, i64 1), align 4, !tbaa !8
  call void @llvm.lifetime.start.p0(i64 4, ptr %2) #5
  store i32 1, ptr %2, align 4, !tbaa !8
  br label %10

10:                                               ; preds = %37, %0
  %11 = load i32, ptr %2, align 4, !tbaa !8
  %12 = icmp slt i32 %11, 1000009
  br i1 %12, label %14, label %13

13:                                               ; preds = %10
  call void @llvm.lifetime.end.p0(i64 4, ptr %2) #5
  br label %40

14:                                               ; preds = %10
  %15 = load i32, ptr %2, align 4, !tbaa !8
  %16 = sub nsw i32 %15, 1
  %17 = sext i32 %16 to i64
  %18 = mul nsw i64 1, %17
  %19 = load i32, ptr %2, align 4, !tbaa !8
  %20 = sub nsw i32 %19, 1
  %21 = sext i32 %20 to i64
  %22 = getelementptr inbounds [1000009 x i32], ptr @d, i64 0, i64 %21
  %23 = load i32, ptr %22, align 4, !tbaa !8
  %24 = load i32, ptr %2, align 4, !tbaa !8
  %25 = sub nsw i32 %24, 2
  %26 = sext i32 %25 to i64
  %27 = getelementptr inbounds [1000009 x i32], ptr @d, i64 0, i64 %26
  %28 = load i32, ptr %27, align 4, !tbaa !8
  %29 = add nsw i32 %23, %28
  %30 = sext i32 %29 to i64
  %31 = mul nsw i64 %18, %30
  %32 = srem i64 %31, 1000000007
  %33 = trunc i64 %32 to i32
  %34 = load i32, ptr %2, align 4, !tbaa !8
  %35 = sext i32 %34 to i64
  %36 = getelementptr inbounds [1000009 x i32], ptr @d, i64 0, i64 %35
  store i32 %33, ptr %36, align 4, !tbaa !8
  br label %37

37:                                               ; preds = %14
  %38 = load i32, ptr %2, align 4, !tbaa !8
  %39 = add nsw i32 %38, 1
  store i32 %39, ptr %2, align 4, !tbaa !8
  br label %10, !llvm.loop !11

40:                                               ; preds = %13
  call void @llvm.lifetime.start.p0(i64 4, ptr %3) #5
  %41 = call noundef nonnull align 8 dereferenceable(16) ptr @_ZNSirsERi(ptr noundef nonnull align 8 dereferenceable(16) @_ZSt3cin, ptr noundef nonnull align 4 dereferenceable(4) %3)
  %42 = load i32, ptr %3, align 4, !tbaa !8
  %43 = sext i32 %42 to i64
  %44 = getelementptr inbounds [1000009 x i32], ptr @d, i64 0, i64 %43
  %45 = load i32, ptr %44, align 4, !tbaa !8
  %46 = call noundef nonnull align 8 dereferenceable(8) ptr @_ZNSolsEi(ptr noundef nonnull align 8 dereferenceable(8) @_ZSt4cout, i32 noundef %45)
  %47 = call noundef nonnull align 8 dereferenceable(8) ptr @_ZStlsISt11char_traitsIcEERSt13basic_ostreamIcT_ES5_c(ptr noundef nonnull align 8 dereferenceable(8) %46, i8 noundef signext 10)
  call void @llvm.lifetime.end.p0(i64 4, ptr %3) #5
  ret i32 0
}

declare noundef zeroext i1 @_ZNSt8ios_base15sync_with_stdioEb(i1 noundef zeroext) #1

; Function Attrs: mustprogress nounwind uwtable
declare noundef ptr @_ZNSt9basic_iosIcSt11char_traitsIcEE3tieEPSo(ptr noundef nonnull align 8 dereferenceable(264), ptr noundef) #2 align 2

; Function Attrs: nocallback nofree nosync nounwind willreturn memory(argmem: readwrite)
declare void @llvm.lifetime.start.p0(i64 immarg, ptr nocapture) #3

; Function Attrs: nocallback nofree nosync nounwind willreturn memory(argmem: readwrite)
declare void @llvm.lifetime.end.p0(i64 immarg, ptr nocapture) #3

declare noundef nonnull align 8 dereferenceable(16) ptr @_ZNSirsERi(ptr noundef nonnull align 8 dereferenceable(16), ptr noundef nonnull align 4 dereferenceable(4)) #1

; Function Attrs: inlinehint mustprogress uwtable
declare noundef nonnull align 8 dereferenceable(8) ptr @_ZStlsISt11char_traitsIcEERSt13basic_ostreamIcT_ES5_c(ptr noundef nonnull align 8 dereferenceable(8), i8 noundef signext) #4

declare noundef nonnull align 8 dereferenceable(8) ptr @_ZNSolsEi(ptr noundef nonnull align 8 dereferenceable(8), i32 noundef) #1

attributes #0 = { mustprogress norecurse uwtable "min-legal-vector-width"="0" "no-trapping-math"="true" "stack-protector-buffer-size"="8" "target-cpu"="x86-64" "target-features"="+cmov,+cx8,+fxsr,+mmx,+sse,+sse2,+x87" "tune-cpu"="generic" }
attributes #1 = { "no-trapping-math"="true" "stack-protector-buffer-size"="8" "target-cpu"="x86-64" "target-features"="+cmov,+cx8,+fxsr,+mmx,+sse,+sse2,+x87" "tune-cpu"="generic" }
attributes #2 = { mustprogress nounwind uwtable "min-legal-vector-width"="0" "no-trapping-math"="true" "stack-protector-buffer-size"="8" "target-cpu"="x86-64" "target-features"="+cmov,+cx8,+fxsr,+mmx,+sse,+sse2,+x87" "tune-cpu"="generic" }
attributes #3 = { nocallback nofree nosync nounwind willreturn memory(argmem: readwrite) }
attributes #4 = { inlinehint mustprogress uwtable "min-legal-vector-width"="0" "no-trapping-math"="true" "stack-protector-buffer-size"="8" "target-cpu"="x86-64" "target-features"="+cmov,+cx8,+fxsr,+mmx,+sse,+sse2,+x87" "tune-cpu"="generic" }
attributes #5 = { nounwind }

!llvm.module.flags = !{!0, !1, !2, !3}
!llvm.ident = !{!4}

!0 = !{i32 1, !"wchar_size", i32 4}
!1 = !{i32 8, !"PIC Level", i32 2}
!2 = !{i32 7, !"PIE Level", i32 2}
!3 = !{i32 7, !"uwtable", i32 2}
!4 = !{!"clang version 19.1.0 (git@github.com:llvm/llvm-project.git a4bf6cd7cfb1a1421ba92bca9d017b49936c55e4)"}
!5 = !{!6, !6, i64 0}
!6 = !{!"vtable pointer", !7, i64 0}
!7 = !{!"Simple C++ TBAA"}
!8 = !{!9, !9, i64 0}
!9 = !{!"int", !10, i64 0}
!10 = !{!"omnipotent char", !7, i64 0}
!11 = distinct !{!11, !12}
!12 = !{!"llvm.loop.mustprogress"}


; Optimized IR (opt -passes='default<O3>'):
target datalayout = "e-m:e-p270:32:32-p271:32:32-p272:64:64-i64:64-i128:128-f80:128-n8:16:32:64-S128"
target triple = "x86_64-unknown-linux-gnu"

%"class.std::basic_istream" = type { ptr, i64, %"class.std::basic_ios" }
%"class.std::basic_ios" = type { %"class.std::ios_base", ptr, i8, i8, ptr, ptr, ptr, ptr }
%"class.std::ios_base" = type { ptr, i64, i64, i32, i32, i32, ptr, %"struct.std::ios_base::_Words", [8 x %"struct.std::ios_base::_Words"], i32, ptr, %"class.std::locale" }
%"struct.std::ios_base::_Words" = type { ptr, i64 }
%"class.std::locale" = type { ptr }
%"class.std::basic_ostream" = type { ptr, %"class.std::basic_ios" }

@d = external dso_local local_unnamed_addr global [1000009 x i32], align 16
@_ZSt3cin = external global %"class.std::basic_istream", align 8
@_ZSt4cout = external global %"class.std::basic_ostream", align 8

; Function Attrs: mustprogress norecurse uwtable
define dso_local noundef i32 @main() local_unnamed_addr #0 {
  %1 = alloca i32, align 4
  %2 = tail call noundef zeroext i1 @_ZNSt8ios_base15sync_with_stdioEb(i1 noundef zeroext false)
  %3 = load ptr, ptr @_ZSt3cin, align 8, !tbaa !5
  %4 = getelementptr i8, ptr %3, i64 -24
  %5 = load i64, ptr %4, align 8
  %6 = getelementptr inbounds i8, ptr @_ZSt3cin, i64 %5
  %7 = tail call noundef ptr @_ZNSt9basic_iosIcSt11char_traitsIcEE3tieEPSo(ptr noundef nonnull align 8 dereferenceable(264) %6, ptr noundef null)
  store i32 1, ptr @d, align 16, !tbaa !8
  store i32 0, ptr getelementptr inbounds (i8, ptr @d, i64 4), align 4, !tbaa !8
  br label %16

8:                                                ; preds = %16
  call void @llvm.lifetime.start.p0(i64 4, ptr nonnull %1) #5
  %9 = call noundef nonnull align 8 dereferenceable(16) ptr @_ZNSirsERi(ptr noundef nonnull align 8 dereferenceable(16) @_ZSt3cin, ptr noundef nonnull align 4 dereferenceable(4) %1)
  %10 = load i32, ptr %1, align 4, !tbaa !8
  %11 = sext i32 %10 to i64
  %12 = getelementptr inbounds [1000009 x i32], ptr @d, i64 0, i64 %11
  %13 = load i32, ptr %12, align 4, !tbaa !8
  %14 = call noundef nonnull align 8 dereferenceable(8) ptr @_ZNSolsEi(ptr noundef nonnull align 8 dereferenceable(8) @_ZSt4cout, i32 noundef %13)
  %15 = call noundef nonnull align 8 dereferenceable(8) ptr @_ZStlsISt11char_traitsIcEERSt13basic_ostreamIcT_ES5_c(ptr noundef nonnull align 8 dereferenceable(8) %14, i8 noundef signext 10)
  call void @llvm.lifetime.end.p0(i64 4, ptr nonnull %1) #5
  ret i32 0

16:                                               ; preds = %16, %0
  %17 = phi i32 [ 1, %0 ], [ %35, %16 ]
  %indvars.iv = phi i64 [ 1, %0 ], [ %indvars.iv.next.1, %16 ]
  %18 = add nsw i64 %indvars.iv, -1
  %19 = add nsw i64 %indvars.iv, -2
  %20 = getelementptr inbounds [1000009 x i32], ptr @d, i64 0, i64 %19
  %21 = load i32, ptr %20, align 4, !tbaa !8
  %22 = add nsw i32 %21, %17
  %23 = sext i32 %22 to i64
  %24 = mul nsw i64 %18, %23
  %25 = srem i64 %24, 1000000007
  %26 = trunc nsw i64 %25 to i32
  %27 = getelementptr inbounds [1000009 x i32], ptr @d, i64 0, i64 %indvars.iv
  store i32 %26, ptr %27, align 4, !tbaa !8
  %indvars.iv.next = add nuw nsw i64 %indvars.iv, 1
  %28 = add nsw i64 %indvars.iv, -1
  %29 = getelementptr inbounds [1000009 x i32], ptr @d, i64 0, i64 %28
  %30 = load i32, ptr %29, align 4, !tbaa !8
  %31 = add nsw i32 %30, %26
  %32 = sext i32 %31 to i64
  %33 = mul nsw i64 %indvars.iv, %32
  %34 = srem i64 %33, 1000000007
  %35 = trunc nsw i64 %34 to i32
  %36 = getelementptr inbounds [1000009 x i32], ptr @d, i64 0, i64 %indvars.iv.next
  store i32 %35, ptr %36, align 4, !tbaa !8
  %indvars.iv.next.1 = add nuw nsw i64 %indvars.iv, 2
  %exitcond.not.1 = icmp eq i64 %indvars.iv.next.1, 1000009
  br i1 %exitcond.not.1, label %8, label %16, !llvm.loop !11
}

declare noundef zeroext i1 @_ZNSt8ios_base15sync_with_stdioEb(i1 noundef zeroext) local_unnamed_addr #1

; Function Attrs: mustprogress nounwind uwtable
declare noundef ptr @_ZNSt9basic_iosIcSt11char_traitsIcEE3tieEPSo(ptr noundef nonnull align 8 dereferenceable(264), ptr noundef) local_unnamed_addr #2 align 2

; Function Attrs: mustprogress nocallback nofree nosync nounwind willreturn memory(argmem: readwrite)
declare void @llvm.lifetime.start.p0(i64 immarg, ptr nocapture) #3

; Function Attrs: mustprogress nocallback nofree nosync nounwind willreturn memory(argmem: readwrite)
declare void @llvm.lifetime.end.p0(i64 immarg, ptr nocapture) #3

declare noundef nonnull align 8 dereferenceable(16) ptr @_ZNSirsERi(ptr noundef nonnull align 8 dereferenceable(16), ptr noundef nonnull align 4 dereferenceable(4)) local_unnamed_addr #1

; Function Attrs: inlinehint mustprogress uwtable
declare noundef nonnull align 8 dereferenceable(8) ptr @_ZStlsISt11char_traitsIcEERSt13basic_ostreamIcT_ES5_c(ptr noundef nonnull align 8 dereferenceable(8), i8 noundef signext) local_unnamed_addr #4

declare noundef nonnull align 8 dereferenceable(8) ptr @_ZNSolsEi(ptr noundef nonnull align 8 dereferenceable(8), i32 noundef) local_unnamed_addr #1

attributes #0 = { mustprogress norecurse uwtable "min-legal-vector-width"="0" "no-trapping-math"="true" "stack-protector-buffer-size"="8" "target-cpu"="x86-64" "target-features"="+cmov,+cx8,+fxsr,+mmx,+sse,+sse2,+x87" "tune-cpu"="generic" }
attributes #1 = { "no-trapping-math"="true" "stack-protector-buffer-size"="8" "target-cpu"="x86-64" "target-features"="+cmov,+cx8,+fxsr,+mmx,+sse,+sse2,+x87" "tune-cpu"="generic" }
attributes #2 = { mustprogress nounwind uwtable "min-legal-vector-width"="0" "no-trapping-math"="true" "stack-protector-buffer-size"="8" "target-cpu"="x86-64" "target-features"="+cmov,+cx8,+fxsr,+mmx,+sse,+sse2,+x87" "tune-cpu"="generic" }
attributes #3 = { mustprogress nocallback nofree nosync nounwind willreturn memory(argmem: readwrite) }
attributes #4 = { inlinehint mustprogress uwtable "min-legal-vector-width"="0" "no-trapping-math"="true" "stack-protector-buffer-size"="8" "target-cpu"="x86-64" "target-features"="+cmov,+cx8,+fxsr,+mmx,+sse,+sse2,+x87" "tune-cpu"="generic" }
attributes #5 = { nounwind }

!llvm.module.flags = !{!0, !1, !2, !3}
!llvm.ident = !{!4}

!0 = !{i32 1, !"wchar_size", i32 4}
!1 = !{i32 8, !"PIC Level", i32 2}
!2 = !{i32 7, !"PIE Level", i32 2}
!3 = !{i32 7, !"uwtable", i32 2}
!4 = !{!"clang version 19.1.0 (git@github.com:llvm/llvm-project.git a4bf6cd7cfb1a1421ba92bca9d017b49936c55e4)"}
!5 = !{!6, !6, i64 0}
!6 = !{!"vtable pointer", !7, i64 0}
!7 = !{!"Simple C++ TBAA"}
!8 = !{!9, !9, i64 0}
!9 = !{!"int", !10, i64 0}
!10 = !{!"omnipotent char", !7, i64 0}
!11 = distinct !{!11, !12}
!12 = !{!"llvm.loop.mustprogress"}


; Effective O3 passes: BDCEPass,EarlyCSEPass,GVNPass,GlobalOptPass,IPSCCPPass,IndVarSimplifyPass,InferFunctionAttrsPass,InstCombinePass,LoopRotatePass,LoopUnrollPass,ReassociatePass,SROAPass,SimplifyCFGPass,TailCallElimPass