Carlos Zenón-Rodríguez and Yabureibo Zenón-Encarnaeión appeal their convictions for violating 18 U.S.C. § 1382 by trespassing on a United States Navy Installation on October 4, 2001. The defendants were protesting the military exercises conducted by the U.S. Navy at and around the Camp Garcia Naval Installation at Vieques, Puerto Rico. They were each sentenced to 180 days in prison, the maximum under the statute. We affirm the convictions.
I.
For the purposes of the Zenóns’ sufficiency of the evidence claims, we describe the facts in the light most favorable to the verdict. United States v. Van Horn, 277 F.3d 48, 54 (1st Cir.2002).
On October 4, 2001, at approximately 11:30 a,m., Puerto Rico police found Carlos Zenón-Rodríguez and his son Yabureibo Zenón-Enearnación on two separate small boats in the waters of Bahia Salinas del Sur (or South Salinas Bay), about 150-200 feet off Camp Garcia, the U.S. military installation on the island of Vieques, Puer-to Rico. The Navy was conducting military exercises on that day and had given prior notice of that fact.
Kathleen Cossairt, a U.S. Navy security liaison, spotted the two civilian vessels earlier that morning from an observation post on Camp Garcia known as O.P. 1. The Rapid Action Force Unit of the Puerto Rico Police Department, “FURA,” was contacted and informed that there were two civilian boats in South Salinas Bay. FURA sent four vessels toward the civilian boats in the bay, which remained about 150-200 feet off shore.
The FURA boats had to chase the Zen-óns’ boats. When the FURA officers reached the Zenóns, the officers informed them that they were in a “restricted area.” The son, Zenón-Encarnación, refused to talk with the officers and told them as *30much. According to one of the officers, the father, Zenón-Rodríguez, told them, repeatedly, “you are our brothers and we don’t want problems with you, but we have to put an end to this.”
After a forty-minute negotiation with the officers, at approximately 12:10 p.m., the Zenóns agreed to leave the area, and did leave, but only after the FURA boats left first. Despite the warnings, the Zen-óns did not leave the prohibited area for some period after the FURA boats left. By this time, they had disrupted the military exercises for about two hours because the range was considered foul while they were in the bay.
When the FURA officers found the Zen-óns in South Salinas Bay, the Zenóns were within the danger zone1 around Camp Garcia outlined in 33 C.F.R. § 334.1470.2
A regular weekly fishermen’s warning notice, which in the normal course is sent to nine locations, was distributed on September 26, 2001, for the week of October 1 to October 7, 2001. The notice is routinely posted in various locations, including the Vieques post office, the Fishermen’s Association, the Port Authority, and marinas in the area. It clearly stated that there would be “dangerous naval activities” in “Danger Area B” from 8:00 a.m. until 11:00 p.m. on October 4. The notice, as it normally does, included a map which depicted Vieques and Danger Area B. South Salinas Bay is in Danger Area B.
The Zenóns were charged with illegally entering naval property in violation of 18 U.S.C. § 1382. They filed a motion to dismiss the indictment on January 3, 2002, which the district court denied on January 14. A one-day bench trial was held on January 15, 2002. After the government rested its case, the Zenóns raised a motion for judgment of acquittal. Fed.R.Crim.P. 29. After hearing argument on the motion, the court denied the motion and found both the Zenóns guilty. The court sentenced each of them to the maximum penalty of 180 days in prison.
Defendants now appeal their convictions. They make four main arguments, which they made previously in their motion to dismiss the indictment and in their Rule 29 motion. First, they argue that the danger zone is not part of Camp Garcia and is not U.S. property, and so they cannot be convicted for trespassing on U.S. naval property under 18 U.S.C. § 1382. Second, they argue that the court erred in not *31granting their Rule 29 motion, because the government did not prove all the elements of the offense charged. Third, they argue that under 33 C.F.R. § 334.3(c)3 they were entitled to at least two weeks’ advance notice of the military exercise and the prohibition from entering the danger zone on October 4, 2001. Fourth, they argue that the regulation creating the danger zone is invalid because it unreasonably interferes with Puerto Rico’s food fishing industry. They say that the district court was obligated to hold an evidentiary hearing on this issue.
II.
A. Whether Ijiewrsions into the Danger Zone May Violate 18 U.S.C. § 1882
Defendants’ primary argument is a territorial one: they say that the danger zone outlined in 33 C.F.R. § 334.1470 is not part of Camp Garcia and is not U.S. property, and so trespassers there may not be prosecuted under 18 U.S.C. § 1382. Defendants claim that because they were in the waters of South Salmas Bay, which is not owned by the U.S. government, they did not violate 18 U.S.C. § 1382.
Whether prosecutions under 18 U.S.C. § 1382 may include trespassers in the danger zone around Camp Garcia is a question of law, and “[w]e review the district court’s construction of a federal statute de novo,” United States v. Maxwell, 254 F.3d 21, 24 (1st Cir.2001). The statute, 18 U.S.C. § 1382, in relevant part, prohibits, “within the jurisdiction of the United States,” entry “upon any military, naval, or Coast Guard reservation, post, fort, arsenal, yard, station, or installation, for any purpose prohibited by law or lawful regulation.” The danger zone regulation itself says that when firing is conducted in the area “no persons or surface vessels ... shall enter or remain within the danger area.” 33 C.F.R. § 334.1470(b).
The defendants’ argument is premised on the erroneous notion that the United States must own the portion of the danger zone where the defendants were found in order to prosecute them for trespassing. In United States v. Ventura-Meléndez, 275 F.3d 9 (1st Cir.2001), this court held that “ ‘government ownership of the property in question is not a requisite to violating Section 1382.’ ” Id. at 17 (quoting United States v. Allen, 924 F.2d 29, 31 (2d Cir.1991)). Instead, “§ 1382 requires only that the government demonstrate either a possessory interest in, or occupation or control of, the area reserved by the military.” Id. Ventura-Meléndez also held that § 1382 extends to prosecution of those who enter a danger zone in *32proximity to a military installation. Id. at 17-18.
In this case, the United States demonstrated its occupation and control of South Salinas Bay in two ways. First, the regulation itself, 33 C.F.R. § 334.1470(a), is such a demonstration. It outlines a large area, which extends from the Camp Garcia beach, and designates it as a danger zone. As we discuss later in the opinion, South Salinas Bay is within the danger zone outlined by the coordinates in the regulation. Second, as a matter of fact, the portion of the danger zone that includes South Salinas Bay was under the occupation and control of the U.S. on October 4, 2001. Cossairt, the U.S. Navy security liaison, testified that there were military exercises occurring on that day, and that South Salinas Bay was in the live impact area. The U.S. Navy observes the area to see if there are intruders and arranges for vessels to apprehend the intruders. Because the U.S. exercised control over the South Salinas Bay area on October 4, 2001, unlawful entry onto that area was prohibited under 18 U.S.C. § 1382.
B. Rule 29 Motion: Elements of 18 U.S.C. § 1382
The Zenóns argue that the court erred in not granting their Rule 29 motion, because the government did not prove all the elements of the offense charged. They say the government presented insufficient evidence to convict them. We review a district court’s denial of a Rule 29 motion de novo. Ventura-Meléndez, 275 F.3d at 17. The defendants have a high burden to meet on an insufficiency of the evidence claim: we affirm the conviction “unless the evidence, viewed in the light most favorable to the government, could not have persuaded any trier of fact of the defendant’s guilt beyond a reasonable doubt.” United States v. Hernandez, 218 F.3d 58, 64 (1st Cir.2000) (quoting United States v. Paradis, 802 F.2d 553, 559 (1st Cir.1986)). The defendants fail to meet this burden.
To prove a prohibited purpose in violation of § 1382, the government must prove that the defendants deliberately entered or remained in the prohibited area without authorization, and that they knew or had notice, actual or constructive, that the entry was prohibited. United States v. Sued-Jiménez, 275 F.3d 1, 6 (1st Cir.2001); Maxwell, 254 F.3d at 24 (explaining that “an unauthorized entry itself can constitute a prohibited purpose” under § 1382; the only state of mind required is a purpose to enter with actual or constructive notice that entry is prohibited). And, because the regulation establishing the danger zone states that “[i]t will be open to navigation at all times except when firing is being conducted,” 33 C.F.R. § 334.1470(b)(1), to prove a violation of § 1382, the government was required to prove that notice was given that the danger zone was closed to the public at the time of arrest. United States v. Ayala Ayala, 289 F.3d 16, 24 (1st Cir.2002). The Zenóns argue that the government did not prove either of these elements.
First, the Zenóns argue that the government did not establish that they entered the prohibited area. They say the government failed to show that either they or South Salinas Bay were within the danger zone outlined in the regulation. Their premise is that the government must “locate] defendants within the longitudes, latitudes and degrees specified in the regulation allegedly violated,” a burden not met here. The argument overstates the government’s burden.
The government provided ample evidence that the defendants were in South *33Salinas Bay, and that South Salinas Bay was within the danger zone. As to the defendants’ location, Sergeant Luis Martinez, one of the FURA officers who intercepted the defendants, testified that he found them in South Salinas Bay, and that his supervisors had earlier informed him that the bay was part of a danger zone. He also testified that he recognized them as “Mr.- Zenon, the father, and ... the son” from seeing pictures of them in newspapers. Another FURA officer, Wilfredo Padilla Sepulveda, who intercepted the defendants, testified that he found the defendants “inside the restricted zone” in South Salinas Bay.
As to the bay being in the danger zone, Cossairt testified that on the morning of October 4, 2001, she saw two civilian boats in South Salinas Bay from her observation point. She pointed out this location on an aerial photograph, which depicted the danger zone. Schedules Officer Ramon DeJe-sus, who supervises the processing of airspace and surface area requests and is responsible for the creation of fishermen’s warnings, also testified that South Salinas Bay is within “Danger Area B,” depicted on the map attached to the fishermen’s warning for the week of October 1 to October 7, 2001. In addition, the court took judicial notice of 33 C.F.R. § 334.1470, which outlines the danger zone in question in this case.
Second, the Zenóns say that they did not know or have notice of the fact that South Salinas Bay was a prohibited area on October 4, 2001, in the sense that the Navy did not alert people to the use of the area for military exercises, and therefore, that it was closed to navigation. In addition to contesting the facts concerning notice, the Zenóns raise one issue of law, which we discuss later, as to the timing of the prior notice required. The government counters that the Zenóns had both constructive and actual notice that entry into South Salinas Bay was prohibited. The evidence supports the government.
Officer DeJesus testified that he is responsible for the creation and dissemination of a weekly fishermen’s warning, which includes, in Spanish and in English, notice of “what areas are to be used [for military exercises] and what areas are off-limits for non-participants.” Such a notice is created and distributed each Wednesday, and includes information about what military exercises, if any, are scheduled for that week. The warnings are regularly sent to, and posted in, nine locations around Vieques and on mainland Puerto Rico. DeJesus testified that a routine weekly fishermen’s notice was sent out on Wednesday, September 26, to all the usual locations. A copy of the warning, in evidence, included information about the military exercises for the week of October 1 to October 7. The notice stated that there would be “dangerous naval activities” in “Danger Area B” from 8:00 a.m. until 11:00 p.m. on October 4. The attached map indicated where Danger Area B was, and South Salinas Bay is within it. Taking the evidence most favorably to the verdict permits the conclusion that the warning was actually posted as part of a regular weekly practice. The fishermen’s warning constituted constructive notice to the Zenóns that military exercises were going to take place in South Salinas Bay on October 4, 2001.
In addition, the Zenóns also had actual notice that their presence in South Salinas Bay, on October 4, was not allowed. Sergeant Martinez informed the Zenóns in their boats that they were in a “restricted area” and that they were not allowed to be there. Officer Sepulveda also said that the FURA-officers , “informed one of them that they could not be there, that this was a *34restricted zone.” Nevertheless, the Zen-óns remained.
The defendants claim that because the FURA officers told them that they were in a “restricted area” and not a “danger zone” the notice was insufficient. Specifically, they say that because the fishermen’s warning referred to a “danger area,” they did not know that they were not allowed in the “restricted area.” The Zenóns attempt to rely on the separate definitions given to a “danger zone” and to a “restricted area” in 33 C.F.R. § 334.2,4 but their argument is to no avail. Whatever the differences, they are not material in this case. The defendants knew from the FURA officers’ warnings that they were not allowed in the area, no matter what the officers called that area.
Because the government presented sufficient evidence to show both that South Salinas Bay was a prohibited area, and that the Zenóns knew or had notice that it was a prohibited area, the district court did not err in denying the Rule 29 motion, and the defendants’ insufficiency of the evidence claim fails.
C. Timing of Notice
The defendants say that the time period for adequate notice is governed by 33 C.F.R. § 334.3(c), which requires two weeks’ advance notice, and here the fishermen’s notice was posted only nine days before October 4, 2001. Section 334.3(c) is simply inapplicable in this case. It only applies to situations in which the military’s expected use of the water area is sufficiently short and infrequent that “formal regulations are not required” and in which a danger zone or restricted area has not been promulgated. 33 C.F.R. § 334.3(c) (2001); see also United States v. de Jesus, 108 F.Supp.2d 68, 71 (D.P.R.2000). Here a danger zone was promulgated. Two weeks’ notice in this case was unnecessary, and the notice which was provided was sufficient.
D. Validity of S3 C.F.R. § 381.11,70
The defendants argue that the indictment should have been dismissed because 33 C.F.R. § 334.1470 was improperly promulgated under 33 U.S.C. § 1, and that it should have been promulgated under 33 U.S.C. § 3, which requires that the regulation will not “unreasonably ... interfere with or restrict the food fishing industry.” 33 U.S.C. § 3 (1994). Because they raised this issue before the district court in their motion to dismiss the indictment, the Zen-óns argue that the district court was obligated to hold an evidentiary hearing on whether the regulation unreasonably interfered with the food fishing industry.
The defendants rely on United States v. Saade, 652 F.2d 1126 (1st Cir.1981). Saade held that the appropriate statutory authority for an almost identical regulation to § 334.1470 was 33 U.S.C. § 3 and not 33 U.S.C. § 1, because § 3 refers more specifically to the promulgation of regulations for the prevention of injuries from target practice. Id. at 1130-32. Saade remanded the case to the district court to hold an evidentiary hearing to determine whether the regulation unreasonably interfered *35with the food fishing industry. Id. at 1133-34. The defendants urge us to do the same here.
In our -view, this case is not identical to Saade. The regulatory context has changed significantly. In 1993, a new provision, explicitly promulgated under 33 U.S.C. § 3, was added to the danger zone and restricted area regulations. See Danger Zone and Restricted Area Regulations, 58 Fed.Reg. 37,606, 37,606 (July 12, 1993). This added provision states:
The authority to prescribe danger zone and restricted area regulations must be exercised so as not to unreasonably interfere with or restrict the food fishing industry. Whenever the proposed establishment of a danger zone or restricted area may affect fishing operations, the District Engineer will consult with the Regional Director, U.S. Fish and Wildlife Service, Department of the Interior and the Regional Director, National Marine Fisheries Service, National Oceanic & Atmospheric Administration (NOAA).
33 C.F.R. § 334.3(b) (2001). Although the danger zone regulation in this case was promulgated under 33 U.S.C. § 1, both regulations are found in part 334 of title 33 of the Code of Federal Regulations, which deals with danger zones and restricted areas. 33 C.F.R. § 334.3(b) applies to 33 C.F.R. § 334.1470, and so the two must be read together, thus satisfying the concern in 33 U.S.C. § 3. Saade seems to have been satisfied by the addition of 33 C.F.R. § 334.3(b). To the extent that the defendants rely on Saade, their reliance is misplaced.
Beyond that, at the district court level the defendants made this argument about the effect on the food fishing industry in only one sentence of their motion to dismiss the indictment. In a nine-page motion they said only that “the Danger Zone in question was improperly promulgated pursuant to 33 U.S.C. § 1, and not 33 U.S.C. § 3 ... and ... the regulation unreasonably affects the food fishing industry in Vieques and Puerto Rico.” In response, the district court said that the defendants did not properly raise the argument because they provided no legal or factual support for it. We agree. For example, the defendants do not anywhere make the argument that the government did not here follow the notification procedure outlined in 33 C.F.R. § 334.3(b). An argument made off-hand in one sentence of a motion is not sufficient to preserve an issue. See United States v. Zannino, 895 F.2d 1, 17 (1st Cir.1990) (“[Ijssues adverted to in a perfunctory manner, unaccompanied by some effort at developed argumentation, are deemed waived”). The defendants did not adequately raise this issue before the district court, and have therefore forfeited the argument on appeal. United States v. Slade, 980 F.2d 27, 30 (1st Cir.1992) (“It is a bedrock rule that when a party has not presented an argument to the district court, she may not unveil it in the court of appeals.”).
III.
The judgment of the district court is affirmed.
. A danger zone is "[a] defined water area (or areas) used for target practice, bombing, rocket firing or other especially hazardous operations, normally of the armed forces. The danger zones may be closed to the public on a full-time or intermittent basis, as stated in the regulations.” 33 C.F.R. § 334.2 (2001).
. 33 C.F.R. § 334.1470 reads:
(a) The danger zone. From Punta Conejo on the south coast of Vieqeus at latitude 18°06'30”, longitude 65°22'33”; thence to latitude 18°03'00”, longitude 65°21'00”; thence to latitude 18°03'00”, longitude 65°15'30”; thence to latitude 18°11'30”, longitude 65°14’30”; thence to latitude 18°12’00”, longitude 65o20'00”; and thence to Cabellos Col-orados on the north coast of Vieques at latitude 18°09’49”, longitude 65°23'27”.
(b) Regulations. (1) It will be open to navigation at all times except when firing is being conducted. At such times, no persons or surface vessels, except those patrolling the area, shall enter or remain within the danger area. Prior to conducting each firing or dropping of ordnance the danger area will be patrolled to insure that no watercraft are within the danger area. Any watercraft in the vicinity will be warned that practice firing is about to take place and advised to vacate the area.
(2) The regulations will be enforced by the Commander, U.S. Naval Forces Caribbean, U.S. Naval Station, Roosevelt Roads, Puerto Rico, and such agencies and subordinate commands as he/she may designate.
33 C.F.R. § 334.1470 (2001).
. 33 C.F.R. § 334.3(c) states:
(c) Temporary, occasional or intermittent use. If the use of the water area is desired for a short period of time, not to exceed thirty days in duration, and that planned operations can be conducted safely without imposing unreasonable restrictions on navigation, and without promulgating restricted area regulations in accordance with the regulations in this section, applicants may be informed that formal regulations are not required. Activities of this type shall not reoccur more often than biennially (every other year), unless danger zone/restricted area rules tire promulgated under this part. Proper notices for mariners requesting that vessels avoid the area will be issued by the Agency requesting such use of the water area, or if appropriate, by the District Engineer, to all known interested persons. Copies will also be sent to appropriate State agencies, the Commandant, U.S. Coast Guard, Washington, DC 20590, and Director, Defense Mapping Agency, Hydrographic Center, Washington, DC 20390, ATTN: Code NS 12. Notification to all parties and Agencies shall be made at least two weeks prior to the planned event, or earlier, if required for distribution of Local Notice to Mariners by the Coast Guard.
33 C.F.R. § 334.3(c) (2001).
. 33 C.F.R. § 334.2 reads:
(a) Danger zone. A defined water area (or areas) used for target practice, bombing, rocket firing or other especially hazardous operations, normally for the armed forces. The danger zones may be closed to the public on a full-time or intermittent basis, as stated in the regulations.
(b) Restricted, area. A defined water area for the purpose of prohibiting or limiting public access to the area. Restricted areas generally provide security for Government property and/or protection to the public from the risks of damage or injury arising from the Government’s use of that area.
33 C.F.R. § 334.2 (2001).