MAA American Mathematics Competitions 2017 Invitational COMPETITIONS TEACHER’S MANUAL A guide for administering the AIME and USA(J)MO COMPETITION DATES: AIME: TUESDAY, MARCH 7, 2017 OR WEDNESDAY, MARCH 22, 2017 USA(J)MO: WEDNESDAY, APRIL 19, 2017 AND THURSDAY, APRIL 20, 2017 Mathematical Association of America PO Box 471 Annapolis Junction, MD 20701 800-527-3690 • amc.maa.org Introduction to American Invitational Mathematics Exam and USA Mathematical Olympiad WELCOME TO THE 2017 COMPETITION 35TH ANNUAL AMERICAN INVITATIONAL MATHEMATICS EXAM AND THE 46TH ANNUAL USA MATHEMATICAL OLYMPIAD What is the American Mathematics Competitions (AMC) Program? The Mathematical Association of America’s (MAA) American Mathematics Competitions program leads the nation in strengthening the mathematical capabilities of the next generation of problem-solvers. Through classroom resources and friendly competition, the MAA AMC program helps America’s educators identify talent and foster a love of mathematics. The MAA AMC program positively impacts the analytical skills needed for future careers in an innovative society. The American Mathematics Competitions are a series of examinations and curriculum materials that build problem-solving skills and mathematical knowledge in middle and high school students. When is the AIME? The AIME I (Main AIME Competition Date) is administered on Tuesday, March 7, 2017. The AIME II (Alternate AIME Competition Date) is administered on Wednesday, March 22, 2017. On competition day, the exam should be administered between 8:45 a.m. to 12:15 p.m. in the school’s US time zone. For time zones outside of the continental US, the exam must be given after 9AM, EDT (UTC-4) on the day of the exam. When is the USA(J)MO? Day one of the USA(J)MO is Wednesday, April 19, from 12:30 PM EDT to 5:00 PM EDT. Day two of the USA(J)MO is Thursday, April 20, from 12:30 PM EDT to 5:00 PM EDT. Three questions are given on each day, participants are expected to compete on both days. Invitational Exam Contact Information: What is the American Invitational Mathematics Examination (AIME)? The AIME is a challenging exam offered to students who excelled on the AMC 10 or AMC 12 exams. The AIME is a 15 question, three hour examination, each answer is an integer number between 0 to 999. The questions on the AIME are more difficult than those on the AMC 10 and AMC 12 competitions. The top scoring students on the AIME are invited to take the United States of America Mathematical Olympiad (USAMO) or the United States of America Junior Mathematical Olympiad (USAJMO), the final examinations before the International Mathematical Olympiad. For any questions regarding AIME Administration, please contact: Email: [email protected] Phone: 800-527-3690 For any questions regarding USA(J)MO Administration, please contact: Email: [email protected] Phone: 202-417-2048 Fax: 202-379-7852 Email contact is preferred. THE MATHEMATICAL ASSOCIATION OF AMERICA’S What is the USA(J)MO? The USAMO and the USAJMO (together referred to as the USA(J)MO) are six-question proof examinations, spread out over nine hours between two days. The top scoring AMC 12 participants (based on a combination of AMC 12 and AIME score) are invited to take the USAMO. The top scoring AMC 10 participants (based on a combination of AMC 10 and AIME score) are invited to take the USAJMO. U.S. citizens and students studying in the United States and Canada (with qualifying scores) are eligible to take the USAMO and USAJMO. 2 | 2017 Invitational Competitions Teacher’s Manual AMERICAN MATHEMATICS COMPETITIONS PROGRAM LEADS THE NATION IN STRENGTHENING THE MATHEMATICAL CAPABILITIES OF THE NEXT GENERATION OF PROBLEM-SOLVERS. Pre-Exam Preparation: AIME How do students qualify to participate in the AIME? Administering the AIME: What You Need To Know Qualification parameters for the AIME vary based on the results of the AMC 10/12 competitions. For each AMC 10, at least the top 2.5% of all scorers are invited, and for each AMC 12, at least the top 5% of all scorers are invited. A cutoff score for AIME qualification will be announced for each exam (10A, 10B, 12A, and 12B) based on the distribution of scores to include these students in the AIME. There is no preset cutoff score for the 2017 AIME. Note that this is a change from previous years. Use these checklists to host a successful AIME competition. How do you prepare students for the AIME? The AIME has a different format than the AMC 10/12: The exam is three hours, all answers are three-digit integers, and there are 15 problems. If you have students who are firsttime AIME qualifiers, make sure to show them the MAA’s AMC resource page so that they can familiarize themselves with the types of problem on the AIME examination. AIME Administration Policy: The AIME must be administered on the official date (March 7, 2017 for the AIME I and March 22, 2017 for the AIME II) to all students. The exam must be administered at the same start time and place for both days. Students who miss the AIME I may take the AIME II. The AIME II is a new set of 15 questions, different from, but comparable to the AIME I exam questions. If you have a student that needs to take the AIME II because they are unavailable to participate in the AIME I, please register for the AIME II. To do this, you can register online for the AIME II at amc-reg.maa.org, or submit an email request to [email protected] for the AIME II by completing the AIME II order form. Please note that there is a processing fee for the AIME II. All AIME II answer forms must be returned by trackable EXPRESS mail service and received by the AMC office by March 28, 2017. AIME Venue Policy: Students should take the AIME at the same testing location where they took the AMC 10/12 whenever possible. This is to ensure that a student’s AMC 10/12 score can be accurately matched with their AIME score for USA Mathematical Olympiad USA(J)MO qualification. In the event that a student absolutely cannot take the AIME at the same competition location, they are to make arrangements with a different competition manager who has the materials to proctor the exam and the new proctor is to complete the Change of Venue form available on amc-reg.maa.org. Students seeking a new venue for AIME participation should reach out to schools nearby, using the Additional Competition Locations tool to look up other AIME host sites nearby. The AMC program will only accommodate change of venue arrangements that have been made between a student and an approved proctor. Pre-exam checklist for AIME: • Confirm with all of your qualifiers that they know they have qualified and the time and place of the examination. • Find the AIME materials that were mailed to you with your AMC 10/12 materials. Instruct your student who qualified for the AIME to complete side 1 of the AIME Student Answer Form using the instructions found on the form. Please carefully follow the marking instructions printed on both the identification form and the student answer form. • Please review all answer forms to ensure that they have been marked correctly. • Students must use their full legal name, no nicknames or abbreviations. It is important for students to pay special attention to marking their name and address accurately. Remind them that student names listed on the AMC website come from this form and this is how they are identified and invited to the USA(J)MO. Once student information has been submitted the AMC program office can not edit any of the information provided on the answer form. • Reserve a quiet room for at least three hours and 30 minutes on the day of the competition, from 8:45 a.m. to 12:15 p.m. in your own (U.S.) time zone, to allow time for pre- and post-examination activities. For time zones outside of the continental US, the exam must be given after 9AM, EDT (UTC-4) on the day of the exam. In extreme cases where you cannot administer the AIME between 7:00 a.m. and 3:00 p.m., please complete the academic integrity pledge form. • Complete the AIME School Identification Form and USAMO/USAJMO Identification Form using the instructions found on those forms. • Review the complete set of examination rules. • Make arrangements to mail the AIME Report Envelopes with a mail service that offers tracking. • The day before the competition, remind students of the time and place of the AIME. • Obtain a supply of #2 pencils with good erasers, unmarked scratch paper, rulers, compasses, protractors and graph paper for your students. Inform students that no aids are permitted other than scratch paper, graph paper, rulers, protractors, and erasers. No AIME questions require the use of a calculator. NO CALCULATORS OR ELECTRONIC DEVICES OF ANY KIND ARE ALLOWED. 2017 Invitational Competitions Teacher’s Manual | 3 AIME Competition Competition Delivery: Watch your email inbox on Monday, March 6, 2017 (after 12:00 noon EDT) for an email from [email protected] with an attachment containing the AIME I exam. If you are proctoring the AIME II exam, this email will arrive on Tuesday, March 21, 2017 (after 12:00 noon EDT). The AIME I and AIME II will arrive as a PDF file attached to the email. Print the competition questions found in the PDF file and make enough copies for each participating AIME qualifier. Administering the AIME: What You Need To Know Use these checklists to host a successful AIME competition. Before the exam • Ensure that you have enough copies of the AIME questions for each of your participating AIME qualifiers. • Seat students so they are separated by an empty space, if possible. • Hand out the previously completed AIME answer forms and provide a #2 lead pencil with a good eraser for each student. • Hand out the printed AIME questions and inform students that they are not to open the packet containing the questions until they are instructed to do so. • Instruct students to read the entire front cover of the AIME exam. Allow 5 minutes for students to review the front cover. • Read aloud the following instructions: • For each question you answer, use a #2 pencil to write your answer at the top of the problem’s answer column. Use 3 digits: each problem has only one correct answer, which is an integer between 000 and 999 inclusive. Then, in each of these columns, blacken the one circle which is labeled with the digit you have written at the top. • DO NOT BLACKEN ANSWERS UNTIL YOU ARE CERTAIN OF YOUR FINAL CHOICE. Forms that contain stray marks may not be read correctly by the scanner that scores the competition. • Ask if there are any questions about examination procedures. Inform students that talking or asking questions during the competition is not allowed. They must do their own work. 4 | 2017 Invitational Competitions Teacher’s Manual • When it is time to begin, tell students to open the packet containing the AIME questions and to be careful to match their answers to the corresponding question. Remind students that there are 15 problems and that they have three hours to complete the competition. Then tell them to BEGIN. During the exam Note to competition managers: The competition should be proctored continuously as you would for any important exam. The person who proctors the exam must warn any students whose eyes wander and disqualify any students caught copying answers or collaborating. Try to provide as quiet an environment as possible. Be sure that no student has access to a calculator or any electronic devices during the competition. • If there is an urgent need to use the bathroom, only one student may leave at a time and the answer form and the AIME questions packet should remain with the competition manager while the student is out of the room. If there is a health or medical emergency, a backup competition manager should be available to assist. • Announce when there are 90 minutes left and when there are 15 minutes left. • When time is up at three hours, tell the students to STOP and have them sign their name in the space provided on the student answer form. • Collect the answer forms and exams as quickly as possible. • Collect all of the AIME question packets following the administration of the competition. As the answer forms are received, check that each student’s name is correct on the form and that it is bubbled in completely. • Inform the students that the competition and solutions may not be discussed with anyone outside of the room either orally or digitally, i.e. email, internet, or social media of any type until after the competition period is over (24 hours after the official competition date). The AIME questions packets must be collected from the students directly after the competition, but they may be returned 24 hours after the competition period is over. AIME Competition After the exam • Please do not grade the answer forms. Send them to the AMC for grading. • Check student answer forms for complete personal information (legal name, DOB, gender, etc.). • Arrange the forms with each form facing the same direction with the same side up. REMOVE ALL PAPER CLIPS, RUBBER BANDS OR NOTE PAPER ATTACHED TO ANY ANSWER FORMS. PLEASE FAN THE FORMS TO SEPARATE ANY THAT MIGHT BE STUCK TOGETHER. • Do not return blank forms or teacher “practice” forms. • Place the AIME School Identification Form on top of the answer forms and insert all forms in the report envelope. • Complete the Certification Form and USAMO/USAJMO Identification Form ask your principal or person with comparable title to sign the Certification Form and complete the rest of the form. • Place the Certification Form in the AIME report envelope with the answer forms, USAMO/USAJMO Identification Form and School Identification Form, seal the envelope and send it by a trackable mail service within 24 hours after the examination has been administered. Schools located outside of the US must return materials by AIR EXPRESS MAIL (DHL, Federal Express, etc.) • Indicate the number of packages you are returning in the space provided on the Report Envelope. • Affix adequate postage to the AIME report envelope. • Note to teachers: The AIME student answer forms sent to the AMC office in Annapolis Junction, MD for grading will not be returned. • After you have delivered all of the answer forms to the school office to be mailed, you may discuss the competition and solutions with your students. Remember that there will be schools taking the competition in other locations. This is why it is important that no one discuss problems and solutions in any online or public forum. AIME Reports: AIME scores, along with PDF certificates of participation and AIME solutions guide, will be emailed to competition managers after the exam has been scored. Please retain this report for future reference in classroom files or with the student counselor office. Many students cite their scores on college applications, and those schools may want verification. The AMC office cannot retrieve or verify student scores. USA(J)MO Qualification Announcements: • The AMC office makes all possible attempts to contact qualifiers and competition managers about USA(J)MO qualification: • Competition managers will be emailed the list of students who took the AIME at their site and qualified for the USAMO and for the USAJMO, and their USA(J)MO student ID numbers needed for all USA(J)MO paperwork. • If the AMC office has been given a legible student email on the AIME answer form, the AMC office will also email these students individually to let them know they have qualified and provide the student with their USA(J)MO ID number. • A list of USAMO qualifiers and USAJMO qualifiers will be posted on the AMC website on Tuesday, April 4, 2017. This list will provide the first initial, last name, school, city, state and grade of each qualifier. • PLEASE NOTE: Some students may appear on this list that had scores below the USAMO and USAJMO cutoff scores. In certain cases, the USA(J)MO committee invites students from unrepresented states. For this reason, please check this list even if none of your students scored above the USA(J)MO cutoffs. • Cutoff scores will be announced on the AMC website on Tuesday, April 4, 2017. If you discover a student with a score above the cutoff who did not receive a student ID number or was not listed on the qualifier list, please contact [email protected] to see if there was an error in matching the student AIME and AMC 10/12 scores. AFTER YOU HAVE DELIVERED ALL OF THE ANSWER FORMS TO THE SCHOOL OFFICE TO BE MAILED, YOU MAY DISCUSS THE COMPETITION AND SOLUTIONS WITH YOUR STUDENTS. 2017 Invitational Competitions Teacher’s Manual | 5 Pre-Exam Preparation: USA(J)MO How do students qualify to participate in the USA(J)MO? Administering the USA(J)MO - What You Need To Know After the AIME I and AIME II are scored, the USA(J)MO committee and AMC program determines cutoff indexes that will qualify students for USA(J)MO participation. The goal is to select approximately 500 students total for the two Olympiads. A student’s USAMO index is defined as their AMC 12 score plus ten times the AIME score. A student’s USAJMO index is defined as their AMC 10 score plus ten times the AIME score. When determining the cutoff index, the USA(J)MO committee considers the difference in difficulty of the various AMC 10/12 A and B exams, as well as the difference in difficulty in the AIME I and AIME II, as determined by score distribution. If this difference is significant, different cutoffs may be announced for different exams. If a student’s scores qualify them for both the USAMO and the USAJMO, they will be invited to take the USAMO. Pre-exam checklist for USA(J)MO: The USA(J)MO committee may choose to invite additional students to take the USAMO or USAJMO. For example, the committee may invite the top scoring student from unrepresented states to take the exam. Only students who are U.S. citizens or attending school in the United States or Canada are eligible to participate in the USA(J)MO How do you prepare students for the USA(J)MO? The format of the USA(J)MO is identical to the format used for the International Mathematical Olympiad. The USA(J)MO consists of six proof-based questions to be solved over two days: three questions will be given on Wednesday, and students will have four hours and 30 minutes to solve them; then three more questions will be given on Thursday, and students will have four hours and 30 minutes to solve the second set of questions. Student answers will be graded for the method of approach, clarity of reasoning, evidence of ingenuity, inventiveness, and general insight. Please make sure students have read the USA(J)MO Instruction Sheet, and look at our AMC Resource Page to prepare for the exam. 6 | 2017 Invitational Competitions Teacher’s Manual Use these checklists to host a successful competition. • Reserve a room for April 19, 2017 and April 20, 2017 from 12:00 p.m. EDT to 5:30 p.m. EDT on both days to allow for pre- and post-exam activities. Note that the competition must be administered starting at 12:30 p.m. EDT and ending at 5:00 p.m. EDT. • If you cannot proctor the students for the entire time on both exam dates, please find an alternate competition manager to assist you to make sure the students are supervised for the duration of both days of the exam. When submitting any forms, provide names and contact information for anyone who helped proctor. • Confirm with participating students that they know their ID number, the date and location of the exam, and that they plan on participating in the competition. Tell all students to arrive in the room by 12:15 p.m. EDT on the day of the exam. The exam must begin at 12:30 p.m. EDT and students cannot be given any additional time past 5:00 p.m. EDT. • Review the exam distribution instructions that were sent via email along with your list of student qualifiers. If you have not received any instructions or a list of qualifiers, and will have students sitting for the exam, email [email protected] as soon as possible. • PLEASE NOTE that unlike 2016, a password is required to download the 2017 USAMO and USAJMO exams from an email sent to competition managers. A test email will be sent to competition managers to make sure they are able to download this pdf in advance of the contest. • In the exam distribution instruction email, competition managers will be given information about the site to ensure they will be able to download the question sets on the day of the exam. If you try to download this sample pdf and are unable to download the sample set of questions, contact [email protected] to be added to the list of proctors who will have the exam emailed to them at 12:15pm EDT on the day of the exam. • Complete the 2017 USA(J)MO Teacher Acknowledgement Form and email the completed form to [email protected] The USA(J)MO office strongly prefers that you scan and email this form to [email protected]. Proctors may also fax the completed form to 202-379-7852. The deadline for this form to be completed is Friday, April 14, 2017. • Either parents, students or competition managers should complete and submit the 2017 Student/Parent Response Form The USA(J)MO office strongly prefers that you scan and email in this form to [email protected]. Proctors may also fax the completed form to 202-379-7852. The deadline for completion of this form is Friday, April 14, 2017. USA(J)MO Competition Administering the USA(J)MO - What You Need To Know Use these checklists to host a successful competition. Before the exam: • Please note that these instructions are for both day one and day two of the USA(J)MO. • Students should come prepared with a lunch and/or snacks since there will be no lunch break during the exam. Make sure that the room has enough working space for students and that students will be free from interruptions. • Before the students arrive, print out plenty of blank USA(J)MO answer sheets. There will be three questions each exam day. Students may require several answer sheets for each of these proof-based questions. • When students arrive in the classroom, ask them to put away all electronic devices. The only materials they may access while they are in the exam room are a ruler, compass, scratch paper, pencil and eraser. • Change to: At 12:15PM EDT, the link to download the exam will be emailed to the USA(J)MO competition manager. Be sure to check your spam filter and refresh your email browser when looking for this message. If by 12:17PM EDT you have not received an email, email [email protected] to have the email re-sent. • Print enough copies of the exam for each of your students. Please be sure to print copies of the USAMO for all USAMO qualifiers, and to print copies of the USAJMO for all USAJMO qualifiers. If your student takes the wrong version of the exam, they will not be given credit for their work. • Before handing out the exam, read the USA(J)MO Instruction Sheet to students. During the exam: The competition should be proctored continuously as you would for any important exam. The competition manager must warn any students whose eyes wander and disqualify any students caught copying answers or collaborating. Try to provide as quiet an environment as possible. Be sure that no student has access to a calculator or calculating device during the competition. • If there is a need to use the bathroom, only one student may leave at a time. Their answer form and contest booklet should be retained by you while the student is out of the room. If there is a health or medical emergency, a backup competition manager should be available to assist. • Announce when there are 3 hours left, 2 hours left, 1 hour left and 5 minutes left. • When time is up at 5:00PM EDT, tell the students to STOP and check that they have labeled the problem number and page number on all of their answer sheets, as well as their USA(J)MO student ID number on every page. • Collect all the students’ exam questions and answer forms following the administration. • Inform the students that the competition and solutions may not be discussed with anyone either orally or digitally, i.e. email, internet, or social media of any type until at least 7PM EDT, the day of the exam. The competition questions must be collected from the students directly after the competition, but they may be returned 24 hours after the competition period is over. • Hand out the exam face down to each student, again making sure that USAMO qualifiers receive the USAMO and USAJMO qualifiers receive the USAJMO. • At 12:30 p.m. EDT, tell the students to BEGIN. WHEN STUDENTS ARRIVE IN THE CLASSROOM, ASK THEM TO PUT AWAY ALL ELECTRONIC DEVICES. 2017 Invitational Competitions Teacher’s Manual | 7 USA(J)MO Competition After the exam: USA(J)MO Grading: Please note that these instructions are for both day one and day two of the USA(J)MO. Each paper is read by as many as four different graders, who agree on a score between 0 and 7 for each question. Every paper is scored against the same standard as every other paper. If a paper was 'borderline' for an award or Mathematical Olympiad Program (MOP) qualification, it will be subject to further scrutiny from graders. Scores will be posted on amc.maa.org on May 5, 2017 by student ID number. All competition managers are emailed student scores that day Students also receive email score reports with their total score, but score breakdowns by question are not available. All scores are final. • DO NOT MAIL IN ANY ANSWER SHEETS TO THE AMC OFFICE UNLESS INSTRUCTED. • Complete the Certification Form for the day of the exam and ask your principal or person with comparable title to sign and complete the Certification Form. • As soon as possible, scan and email the Certification Form and student answers to [email protected]. If you cannot scan and email these forms, fax them to 202-379-7852. • When emailing the form and student answers, use the subject line: Answer Sheets - Day (1 or 2), IDs (List all student IDs) • If multiple students participated, when possible please upload each student’s answer sheets as separate files. For example, if two students took the exam, email two pdfs, one for each student. • The AMC office will check every certification form and every answer sheet to make sure that it is complete and legible. Due to the large volume of responses, it may take up to 48 hours per exam day to confirm receipt of all answer sheets. It may take an additional week to confirm that every page of every answer sheet is legible enough for grading. For this reason, we ask that competition managers keep student answer sheets for at least seven days after the second day of the exam. 8 | 2017 Invitational Competitions Teacher’s Manual USAMO Winners: The 12 top-scoring students on the USAMO will be invited to attend an award ceremony held in Washington, D.C. on June 5, 2017. Activities include a reception at the Mathematical Association of America headquarters and a celebration dinner with the mathematical sciences community. These 12 students are emailed May 5, 2017 with details about the awards ceremony and their names and schools are announced online. Mathematical Olympiad Program (MOP): The MOP is an invitational summer program for the US International Mathematical Olympiad (IMO) team and top scoring USAMO and USAJMO students. These students are invited to enter a further series of Olympiad-style tests that will determine the following year's IMO team. The Mathematical Olympiad Program takes place June 6–July 1, 2017 on the campus of Carnegie Mellon University. Students take classes on advanced mathematical topics, meet special guest speakers, train for mathematical competitions, and participate in related social and mathematical activities. Students who are invited to MOP receive emails on May 5, 2017 with details about the program and all necessary forms. A very small number of additional students may be sent invitations after May 5 if any invited students are unable to attend MOP. AMC Policies Policy for Changes: The Committee on AMC may, from time to time, change the program rules, regulations, awards and conditions of participation in whole or in part. Whenever possible competition managers will be notified of these changes ahead of time. Early administration is NEVER permitted and will lead to a disqualification of the results. Such an administration would jeopardize the validity of all scores from other schools. Official administration: The only official days for the AIME are March 7 for the AIME I and March 22 for the AIME II. The only official days for the USA(J)MO are April 19 and April 20 from 12:30 p.m. EDT to 5:00 p.m. EDT. Only official AIME participants are eligible for participation in the USA(J)MO and only official USA(J)MO participants will be scored. Please note that if the AIME is administered in a time zone outside of the continental US the examination must begin after 9:00 a.m. EST on the official competition day. Competition Proctoring • The proctoring of both the AIME and the USA(J)MO should be by a teacher (preferably a mathematics teacher) or administrator at the school; a college or university teacher of mathematics, or a responsible adult who is a math club or team coach, and not related to any of the participants. • The proctoring of the competition must take place in a public building, (i.e., school library, college or university, church, etc.). • All students must take the competition at the same time, either in one group or in separate classrooms and be under the supervision of a proctor. • The proctor should not be related to any of the participants. Under no circumstances may a parent proctor an exam for their child. Students with Accommodation Plans (e.g., for Visual or Learning Disabilities): If an AIME-qualified student is visually impaired and/or learning disabled, contact the AMC office at [email protected] to discuss accommodations. Unfortunately, the AIME is not available in braille. The time allowance for students with learning disabilities is four hours and 30 minutes. If a USA(J)MO qualified student is visually impaired and/or learning disabled, contact the USA(J)MO office at [email protected]. Questionable Scores: If it is clear to the competition manager from personal observation that a student has cheated, then the competition manager must disqualify the student. If the competition manager receives an accusation or obtains indirect evidence of cheating, then the manager must hold back the student’s paper and immediately report all the facts of the situation to the AMC Director, who in conjunction with the Committee on AMC, will determine what to do. UNDER NO CIRCUMSTANCES may the school decide on its own to accept a questionable score. GOOD LUCK TO YOUR STUDENTS ON THE 2017 AIME & USA(J)MO! We hope they find the competitions challenging and exciting. 2017 Invitational Competitions Teacher’s Manual | 9
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