US2371156A - Ladder - Google Patents

Description

March 13, 1945. N. L. DAHLANDER v 2,371,156

LADDER Filed Nov. '6, 1942 2 Sheets-Sheet 1 Hill "lllllll ATTORNEY March 13, DAHLANDER 2,371,15

-' LADDER Filed Nov. 6, 1942' 2 Sheets-Sheet 2 INVENTOR' W 7 ATTORNEY Patented Mar. 13, 1945 LADDER Noel L. Dahlander, New York, N. Y., assignor of one-half to Robert J. Earl, New Canaan, Conn.

Application November 6, 1942, Serial No. 464,713

9 Claims.

and more especially to ladders composed of metal or the like. i i

Among the objects of the invention it is aimed to provide an improved ladder having flexible suspensory elements such as chains and extensible rungs serving not only to reinforce the rungs at points therein where the greatest bending stresses and strains are received, but also to enable lengthening the same at will to suit the emergency or use to which the ladder is to be put.

It is still anotherpbject of the present inven tion to provide animprovement in ladder construction that will serve not only to the benefit of a single ladder or Jacob's ladder, but also benefit a multiple ladder for use in disembarking from the side of a vessel in case of an emergency, resulting as an instance from the bombing or torpedoing of the vessel on which the ladder is equipped. I

These and other features, capabilities and advantages of the invention will appear from the This invention relates to ladders in general subjoined description of specific embodiments 1 thereof illustrated in the accompanying drawings in which Figure 1 is a front elevation of a multiple ladder equipped according to one embodiment of the present invention.

Fig. 2 is an end elevation of the ladder shown in Figure 1. l Fig. 3 is a front elevation partly in section of a rung with its associated parts made according to one embodiment of the invention, on a larger scale than that shown in Figure 1.

Fig. 4 is a plan view partly in section of the parts shown in Fig. 3 on the same scale as used in Fig. 3.

ing to the embodiment illustrated in Fig. '7 on a smaller scale than that used in Fig. 7.

Fig. 11 is a fragmental frontelevation of a rung and its associated parts made according to still another embodiment of the present invention, on a scale slightly less than the scale of Fig. 10.

Fig. 12 is a fragmental plan view of .the parts shown in Fig. 11 and on the same scale as that used in Fig. 11.

Fig. 13 is a fragmental front elevation of a rung and its associated parts of still another embodiment of the present invention using the same scale as that used in Fig. 11.

Fig. 14 is a fragmental plan of the parts shown in Fig. 13, using the same scale as that used in Fig. 13. 1

In the embodiment shown in Figures 1 and 2, there is shown a multiple ladder l, illustrated more or less diagrammatically consisting of a plurality of suspensory or longitudinally extending flexible elementsor members, in the present instance consisting of the chains 2 composed of links such as the links 3, conventionally known as the lock link type or pattern, although obviously good results would under certain circumstances no doubt also be obtained with other Fig. 5 is a section on the line 5--5 of Fig. 3

on the same scale as used in Fig. 3. i

Fig. 6 is a fragmental exploded perspective of the outer end portions of the complemental parts of a single rung made according to the invention shown in Fig. 3 on the same scale'as used in Fig. 3. 1 i

Fig. 7 is a front elevation of a rung andassociated parts partly in section made according to another embodiment of thepresent invention on the same scale as used in Fig. 3.

Fig. 8 is a section on the line 8--8 of Fig. 7 on the same scale as used in Fig; 3. Fig. 9 is a fragmental plan of .a portion of a rung, as a blank, before being bent into shape, on the same scale as used in Fig. 3. Fig. 10 is a .perspectiveoi arung made.accord-.

types of links such for instance as the Tenso type or pattern,

These chains 2 each have a ring d secured to the uppermost link as shown in Figures 1 and 2 to receive ropes or lanyards for lashing rings 4 and thereby the multiple ladder I to the railing of the vessel with which the ladder is to be used. In the present instance, the suspensory elements I, have connected thereto the transversely extending rungs 5 which with their connections to the suspensory elements I constitute the main part of the invention with regard to the embodiment illustrated in Figures 1 to 6, inclusive.

Each rung consists essentially of two telescopic members, as an instance the member 6 slidably mounted in the member 1. The members 6 and 'l in this embodiment are preferably composed of sheet metal of a predetermined thickness, a shell having a thickness of .025 inch to .0375 inch being satisfactory under ordinary circumstances.

The shell 6 as shown in section in Fig. 5 is U also the connecting web 13 and the flanges I4 and 15 extending parallel to the web I3 and formed at the ends of the webs H and I2 to engage and slidably receive the outer face of the web H] of the section 6. As shown, the widths of the webs 8 and 9 correspond to the distances between the web l3 and the flanges l4 and I5, respectively, so as to enable the section 6 slidably to be mounted in the section 1. When assembled, the webs l3 and H) of the sections 1 and 6, respectively, form opposite walls of a rectangular chamber. To the outer end of the section 6 there is secured the bracket l6, such bracket in the present instance shown as having two parallel arms I1. and I8, respectively, to engage the outer faces of the webs 9 and 8, respectively, as particularly shown in Figs. 3 and 4. The arms If! and I8 form parallel elements of a substantially .U shaped construction having the intermediate portion l9 provided with an arcuate extension-2D curving outwardly away from the free end of the section 6 and registering with the indentation 2| formed in'the web ID of the section 6 so as to clear the shank 22 of the link 3 of a suspensory element 2. In order to secure the bracket Hi to the section 6, there are preferably provided the screws 23 and 24 extending from the arm l8 through regis tering openings in the webs 8 and 9 and arm respectively, the screws 23 and 24 being preferably threadably connected to the arm H and then the outer free end burred finally to "anchor the screws 23 and 24 against displacement. The adjacent end of the section 1 has recesses 25 and 26 formed in the webs and |2, respectively, so as to clear the arms I8 and I7, respectively, when the position of the section 6 relative to the section 1 is similar to or approaches the position shown in Fig.5.

The outer end of the section 7 is also provided with a bracket 21 similar to the bracket l6 having the arms 28 and 29 secured to the outer faces of the webs 'l2'and I respectively. The arms 28 and 29 form the parallel arms of a substantially U shaped member having an intermediate web portion30 provided with an outwardly curved arcuate portion 3| registering with the indentation 32 formed in the web l3 of the section I in order to aiford suflicient clearance for the shank 33 0f the link 3 of the suspensory element 2. The arms 28=and 29-are also connected to one another and to the webs 2 and M, respectively, by suitable securing means, in the present instance shown as the screws 34 and 35, respectively, the screws 34 and 35 extending through registeringopenings formed in the arm 29, web web I 2 and arm 28.having screw threaded connections with the arm28 and burred at their outer free ends as shown at 3B and 31, respectively. The end of the section 6 adjacent to the bracket 21 for closed position is provided with slots-38 and 39 in the webs 8 and- 9,respectively, wide enough to clear the shanks of the screws 34 and 35 when the sections 6 and l are moved into the position shown in Fig. 501' into a position approaching that shown in Fig.5.

The brackets; and 2! are preferably composed of sheet metal having a thickness of about .1250 inch for ordinary use.

In order to anchor the sections 6 and I of a rung at a predetermined position, according to the use desired, there are provided the bolts 40 and the openings 4| in the section 1 and the openings 42 in the section 6. The openings 4| are shown formedin the web l3 of the section 7, and the openings 42 are in the web IU of the section 6. The openings 4| are spaced from one another aipredetermined distance, a distance of about one inch for a rung section about ten inches in length. When the spaces between the openings 4| are predetermined at one inch, then obviously the spaces between the openings 42 are predetermined a corresponding distance. For locking the two sections 6 and 1 to one another, only two bolts 40 are necessary, one to connect the inner slotted end of the section 6 to the section]. and therother to connect the slotted end of thesection 1 tothe section .6. l In-such case the bolt 40 at the left hand end of Fig. 3 extends through an opening 4| formed in the web I3 which registers with an opening 42 formed in the web l0 and the outer end of the bolt provided with a nut 43 to anchor the same in place. Sim ilarly see .the right hand end of the section 1 in Fig. 3, inorder to secure it to the section 6 the bolt 40 will pass through an opening 4| formed in the web |3 of the section 1 which registers with an opening 42 formed in the web 10 of the section 6, the bolt extending through the opening 42 and projecting beyond the outer face thereof to receive the nut 44.

While it is possible to conceive a case where it is desired to extend therung the full distance where the sections 6 and I merely have their inner ends overlapping, such maximum extension will be rare. Ordinarily, the variation in length will be very limited. As an instance, if the disembarkment isto take place for passengers or soldiers without equipment, then'the section 6 may be fully closed upon one another to form the minimum extension. However, if it is desired to disembarka troop of soldierswith equipment, as for instance a troop of commandoes, then it might be desirable to extend the rungs at least three inches. In'such case it will appear that the middle of the rungwhich'will'receive the greatest bending force will be practically double the shell thickness due to the 'overl-appingportions of the sections 6 and 1 than will be the end portions'of the sections =6 and I adjacent the'suspensory elements-2 where the bending force will be least. As a' matter of fact,even when the sections 6 and I are stretched out almost' to their limit, the middle of the rung will still have the overlapping portions of the sections 6 and-1 and thereby protect thatportion of the rung, the middle, which will ordinarily be subjected to the greatest bending strain or stress resulting from the engagement thereof by the foot of the disembark-ing passenger or soldier.

In other words, according to the invention, a maximum'flexibility is afforded'to convert the rungs of a single ladderor'multiple ladder either into a short rung one long rung according to the use contemplated; but also maximum reinforcement provided for the portion of the rung which is subjected to the greatest'bending strain 'or stress during use.

With the-embodiment shown in Fig. 6 the pivotal connections between the links 3 and the brackets l6 and'z'l serve the same purpose as the flexibleconnections between the rungs and suspensory members shown in my co-pending application, Serial -'No. '447,529, to compensate for tion between the suspensory members 2 and the rungs, as for instance, when these ladders are used to extendfrom the deck of a vessel to an upright, such as the upper ends of a davit, in which case one end of the multiple ladder is lashed or secured to the deck ofthe vessel and the other end secured to the upper end of the davit or upright. For this purpose the embodiment illustrated in Figs. 7 to is particularly suited. In this embodiment instead of a rung, rectangular in cross section, there is provided a rung 45 substantially triangular in cross section. This rung 45 is also composed of two sections, an inner section 46' and an outer section 41 telescopically slidable one upon the other. The section 46 has an upper intermediate web 48 and two convergent webs 49 and 56 extending from the web 48 and engaging one another at their free edges as shown in Fig. 8 to form a chainbered body, triangularin cross section. The sections 46 and 41 are preferably composed of sheet metal and before being bent into the chambered form shown in Fig. 8, they are preferably formed into plane blanks, Fig. 9, showing the right hand outer end of the section 46 before being bent into shape. In Fig. 9, the blank of section 46 is shown as provided with a slot 5| formed in the middle of the web 48 and extending from the free edge thereof .to a distance of about one inch in full size. The webs 49 and 50 in turn have recesses 52 and 53 cut out of their corners and extending inwardly from the free outer end of the section 46 a distance corresponding with the length of the slot 5|. In bent form, that shown in Fig. 8, the slot 5| will aline With a common slot formed by the recesses 52 and 53. The section 41 consists of an intermediate web 54 and two lateral converging webs 55 and 56. The web- 54 as shown in Fig. 10 is also provided with a slot 51 similar to the slot 5|, and the webs 55 and 56 also provided with recesses 58 and 59, respectively; similar to the recesses 52 and 53, the recesses 58 and 59 forming with one another a common slot in alinement with the slot 51 when the webs 54, 55 and 56 are bent into the shape shown in Fig. 10. The widths of the webs 48,- 49 and 50 are slightly less than the widths of the webs 54, 55 and 56, so that the section 46 in bent form will slidably fit inside of the section 41. The sections 46 and 41 may be locked in any predetermined extended position by bolts, such as the bolts 60. To receive such bolts 66, the webs 55 and 56 are provided with alined openings 6| and 62, respectively, the openings 6| being formed in the web 55 and the openings 62 being formed in the web 56. The openings 6| in the web 55 and the openings 62 in the web 56 are spaced from one another'a predetermined distance, a distance of one inch being satisfactory for ordinary uses.

The webs 49 and 56 of the section 46 are provided with rows of alined openings 63 and 64, respectively, each opening 63 being alined with one opening 64. Furthermore, the openings in each of these webs are spaced a predetermined distance from one another, depending upon the distance that the openings of the webs 55 and 56 are spaced from one another so that the sections 46' and 41 may be positioned to enable the sets ofopenings 6| and 62 of the section 41 to aline with the openings 63 and 64 of the section 46. When these sections 46 and 41 are so positioned that their respective openings are in alinement with one another, then the bolts 66 may be introduced, a ,bolt 66 passing as an instance through a set of alined openings 6|, 63, 64 and 62 toproject beyond the outer face of the web 56 there to receive a nut 65. In order to form a proper gripping surface for the bolt, the head of the bolt 60 and the nut 65, preferably the insertions 66 and 61 are provided, the insertion 66 having an inclined face to engage the outer face of the web and the insertion 61 having an inclined face to engage the outer face of the web 56..

When the sections 46 and 41 are once positioned to form the length of rung desired, then one or more bolts 69 may be inserted. In Fig. 10 two bolts are provided, one engaging the set of openings 6| and 62 nearest the right hand end of the section 41 which are then in alinement with a pair of openings 63 and 64 in the section 46, and another bolt 66 engaging the openings 63 and 64 nearest the left hand end of the section 46 which are then in alinement with a pair of openings 6| and 62 in the section 41. In this.

embodiment it is, of course, obvious that under some circumstances, merely one bolt 66 may be sufiicient to anchor the two sections 46 and 41 to one another. In such cases it is preferable to insert the bolt 66 in the sets of openings which register with the sets of openings 63 and 64 nearest the left hand end of the section 46 since obviously if the bending force is exercised on the web 54 and between the right hand end of the web 54' and the bolt 6|], any additional bolts will contribute very little to relieve the strain on the bolt 66 farthest to the left. Any additional bolts 60, however, will serve as reinforcements.

In this respect it is of course obvious that the construction illustrated in Fig. 3 can similarly be suitably anchored for some uses bya single bolt 46, preferably if it engages the set of openings nearest the left hand end of the section 6 which are then in alinement with openings 4| in the section 1. However, in the interest of reinforcement, obviously the flanges l4 and I5 of the embodiment illustrated in Fig. 5 would be materially relieved of their load if a plurality of bolts 40 were provided throughout the length of the rung 5 of the embodiment shown in Fig. 5.

To return to the embodiment in Fig. '7, however, the slot 5| and common slot formed by the recesses 52 and 53 are provided to receive a link 3 of the suspensory element 2. Similarly, the slot 51 and common slot formed by the recesses 58 and 59 are provided to receive a link-3 of suspensory element 2. When the links 3 are so received in the slots of the sections 46 and 41 both the shanks 65 and 66 are disposed in a pair of registering slots and anchored against a pivotal motion with respect to the sections 46 and 41.

To anchor the links 3'in the slots of the sections 46 and 41 against lateral displacement, pref erably a disc such as the disc 61 on the end of the section 46 and such as the disc 68 on the end of the section 41 are provided. The disc 61 is provided with a triangular opening to receive I the end of the section 46 and then preferably thefree end 69 of the section 41 is burred over to lock the disc 61 in place. In turn, the disc 68 is provided with a triangular slot corresponding in size to the cross section of the section 41 to receive the end thereof whereupon the extion asshown in Fig; 63, triangular in cross section as shown in Fig. 10, or .assume any. one of a number of other forms in orosssection, it is assumed for the purpose of this description that they will partake of the triangular cross section shown in Fig. 10. These'sections arexprovided with openings registering with one another to receive bolts such as the bolts 141 similar to the bolts 40 of the embodiment illustrated in Fig. '3. This embodiment, however, is particularly adapted for use in a multiple ladder where the adjacent rungs in alinement with one another arepivotally mounted relative to one another .on the suspensory elements 15. The pivotal connection of. these rungs H with the suspensory elements l5 constitutes the main feature of this embodiment and will now be described. .It consists of plugs 16 and TI, plug 16 as an instance being anchored in place in theend of the section l3 by a bolt such as the bolt 18, and the :plug H in turn being anchored in place in the end of the section 12 by bolts such as the bolt l9. The plugs 16 and 11 have outward extensions 80 and 8,], respectively, having openings 82 and 83, respectively, freely to receive the shanks 84 and 85, respectively, of the link 86 .of the suspensory element 15.

In order to provide spacers for spacing the rungs from the side of the vessel for the embodiment illustrated in Figs. 11 and 12, disks ='8'1 similar to the disks 6'! and 68 are mounted on the ends of the sections 12 and 1.3.

In the embodimentshown in Figs 13'and'14, again there is illustrated a fixed connection between the rungs of the suspensory elements. Here too the rung, as an instance 88, is composed .of two sections 89 and 90 telescopically slidable one upon the other, and for the purpose of this description assumed to be triangular in cross section similar to that shown in Fig. 10. The means for anchoring the sections 89 and 90 in'adjusted position is similar to that illustrated in Figs. 7 to by means of a bolt such as the bolt 9l. Here the outer ends of the sections '89 and 90 are slotted as is the case with the sections 41 and 46, respectively. However, in this embodiment the ends of adjacent alined rungs 88 have the outer slotted ends of a section 89 overlapping the outer slottedend of an adjacent section 90, and then a boltsuch as the bolt 92 pass through the two overlapping ends of the sections 89 and 9|] to anchor the same in place. Here the alined slotted ends of overlapping portions of the sections 89 and 80 will register to form a common pair of slots for the shanks 93 and 94 of a link 95 of a suspensory element toanchor such rung 95 against pivotal movement relative to the rungs B8. In order to provide spacing means for the rungsBB of this embodiment, 'disks'96 may be mounted on the slotted ends of the sections 89 and secured in place as is the case with the disks 8'! and 68 of the embodiment shown in Fig. '7. While the embodiments shown in Figs, ll-to 14, inclusive, are particularly adapted for multiple ladders, it is obvious that the embodiments illustrated inFigs. 3 and 7 may be adopted either for multiple ladders or for single ladders of the type known as the Jacobs ladder.

It is obvious thatvarious changes and modifications may be made to the details of construction without departing from the general spirit of the invention as set forth, in the appended claims.

Obviously in place of burringthe ends of screws and rungs tozanchorpartsqazamst"displacement, spot welding :may beusedtaeood advantage.

Obviously, also, the section rli, of the ,embodlment used in Fig- 5 may have inwardly extending flangescat the free ends .of thewebsfl anda! such ,as the flanges and liatthe ends of the webs and 12 without departing from the spirit of the invention. 1 1 it is obvious, of course, also, that the hollow. chambered triangular bar illustrated in Fig. 10, as an instancapresents decided advantages over a hollowcylindricalbar as; an instance, not only to increasestrength andrigiditmbut also as to bearing surface .for ,the 'feet and better hand grasp, and reduction inmaterialascompared,as an instance, to .a chambered cylindrical bar.

IcIaim': 1. ,In a ladder, thecombinationof. flexible suspensory elements composed of-metal chain links,

extensible rungs, each including two rigid sheet metal telescopingmembers bent into chambered bars polygonal in cross section, one chambered bar being slidable within the othensaid other chambered bar having a plane upper tread forming wall, means for positively anchoring the chambered bars ofeach rung .to one another to for .a predetermined length .of rung, there being vertically alinedopenings in the opposing wall portionsof the outer free end of each bar. to receivea link of one of said suspensory elements, edges ofthe openings ,of the wallportionsanchoring the links of suspensory elements against radial displacement,- and meansanchored on said free ends against axial displacement and adjacent tosaid links to-ancho said suspensory elements against axial displacement.

2. Ina ladder, the combination of flexible suspensory elements composed of metal chain links, extensible rungs each including two'rigid sheet metal members bent into chambered bars polygonal in cross section, one chambered bargrbeing slidable within theother, said other chambered bar having a plane upper tread forming wall, means foranchoring the chambered bars of each rung to one anotherto form a predetermined length of rung, there being vertically alined slots in the free ends of said chambered barsv to receive and anchor a link of a suspensoryelement against radial displacement, and means including spacer disks and, burrs on the free ends of said bars for anchoring a link disposed in a slot against axial displacement.

, In a ladder, the combination of flexible suspensory elements'composed of metal chain links. extensible rungs eachincluding tworigid sheet metal members bent into chambered bars, one chambered bar being slidable within therother, means for anchoring the chambered bars of each rung to one another to form apredetermined length of rung, there being slots inv the free ends of said. chambered bars, the adjacent free ends of adjacent rungs overlapping withtheir slots in alinement to receivea link, and means for anchoringsuch adjacent freeends of adjacent bars to one another with the link secured thereto.

4. In a ladder, thecombination of flexible suspensory elements composed of. metal chain links, extensible rungs each including. two, rigid sheet metal telescoping members bent into chambered bars polygonal in cross section, one chambered bar being slidable within the othensaid other chambered bar having; a plane upper tread form-,

- ing wall, means for anchoring .thechambered bars'ot each rung to one another to form apredetermined lengthoi rung,.there being vertically alined openings in the opposing walls ofthe free end of each bar to receive a link of one of said suspensory elements, edges or the openings of said walls anchoring links of the suspensory elements against radial displacement, and spacer disks mounted on said free ends against axial displacement and adjacent to said links to anchor said suspensory elements against axial displacement.

5. In a ladder, the combination of flexible suspensory elements composed of metal chain links, extensible rungs each including two, rigid sheet metal telescoping members bent into chambered bars triangular in cross section, one chambered bar being slidable within the other, said other chambered bar having its intermediate wall forming a plane upper tread, means for anchoring the chambered bars of each rung to one another to form a predetermined length of rung, there being vertically alined openings in the opposing wall portions of the free end of each bar to receive a link of one of said suspensory elements, edges of the openings of said bars anchoring links of the suspensory elements against radial displacement; spacer disks, each spacer disk having atriangular opening conforming to and receiving the free end of a bar and anchoring the link of a suspensory element against radial displacement, and burrson the free ends of said bars for anchoring said'spacer disks and said suspensory elements against axial displacement.

6. In a ladder, the combination of flexible metal suspensory elements, extensible rungs, each including two rigid sheet metal telescoping members bent into chambered bars-one chambered bar being slidable within the other, said other chambered bar having a plane upper tread forming wall, there being a plurality of openings in each chambered bar, the openings in one chambered bar being spaced from one another a distance corresponding to the spaces between the openings in the other chambered bar to en- 7. In a ladder, the combination of flexible metal suspensory elements, extensible rungs each including two rigid sheet metal telescoping members bent into chambered bars polygonal in cross section, one chambered bar being slidable within the other, the outer bar having a substantial plane upper surface to form a tread, and means for positively anchoring the chambered bars of each rung to one another to form a predetermined length of rung, there being vertically aligned openings in the opposing wall portions of the outer free end of each bar to receive one of said suspensory elements, .edges of the openings of said wall portions anchoring the suspensory elements'against radial displacement, and means including spacer disks and bars on the free ends of said bars for anchoring said suspensory elements against axial displacement.

8. In a ladder, the combination of flexible metal suspensory elements, extensible rungs each including two rigid sheet metal telescoping members bent into chambered bars triangular in cross section, the outer bar having a plane upper tread surface and two inwardly extending flanges to form slideways for the inner bar, means for anchoring the chambered bars of each rung to one another to form a predetermined length of rung, there being a recess in the tread surface of the'free end of each bar and complemental recesses in the free ends of the flanges of each bar in alinement with the recess in its tread surface to receive one of said suspensory elements, edges able the openings of the two bars of a rung to register with one another, and means extending through alined openings of the bars of a rung to anchor the bars to one another to form a predetermined length of rung, there being vertically alined openings in the opposing walls of the outer free end of each'bar to receive one of said suspensory elements, edges of the openings of said walls anchoring the suspensory elements against radial displacement, spacer disks, each spacer disk havingan opening conforming a? and receiving the free end of one of said bars to anchor a suspensory element against axial displacement, and burrs on the free ends of said bars to anchor said spacer of the alined recesses of said bars anchoring the suspensory elements against radial displace ment, spacer disks, each spacer disk having a triangular opening conforming to and receiving the free end of a bar to anchor a suspensory element against axialdisplacement; and means on the free ends of said bars to anchor said spacer disks against axial displacement.

9. In a ladder, the combination of flexible metal suspensory elements, rungs composed of rigid sheet metal bent into chambered bars triangular in cross section, the intermediate web of the bars constituting the tread surface with the end webs converging toward one another, there being a recess in the freeend of each intermediate web and complemental recesses in the converging webs in alinement with the recess in said inter mediate web, edges of the alined recesses anchoring the suspensoryelements against radial displacement, and means including spacer disks and burrs on the free 'ends of said bars for anchoring the free ends of the bars to said suspensory elements.

NOEL L. DAHLANDER. f

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