More information can be found here.
Background
When European golf Federation - EGA - in 1997 decided that Europe golf countries would use the American Course Rating and Slope System to describe golf difficulty of a golf course, was the foundation created to shape a common European handicap system - EGA-handicap system. This was introduced in Latvia 2009.
This short presentation is to introduce members of Latvian Golf Federation to EGA handicap system and does not fully cover all aspects of the system.
With EGA-handicap system we play against the courses Par and not on the Course Rating which is called SSS (Standard Scratch Score). The EGA system has a Course Rating built into conversion tables. This principle is now gradually penetrated throughout Europe except the British Isles.
Any golfer - woman as a man - can in private sessions choose which course (tee set) they will play from and the conversion table tells how many extra strokes (playing Hcp or sHCP) they will get with their exact EGA Hcp (eHCP). Tournaments rules set indication of the tee set to be played off and LGF recommendation is to be as liberal as possible with this as golf has such wide gap of ages of participants.
EGA-handicap system's purpose is also to generate correct handicaps that reflect the player's scoring potential and which allow players with different handicaps to compete on an equal footing, adapted to course difficulties. Unlike American handicap system it is not a player's average scoring that is basis for handicap setting but the potential scoring capacity that is measured by eHCP.
Handicap is determined on the basis of merit, where high scores on each hole reduced by using the Stableford points, since these high scores do not reflect the player's actual potential.
Scores from tournament results apply to handicap regulations.
For players with handicaps higher than 4.5, also scores of private rounds better than handicap and so-called "Extra Day Scores" are changing handicaps according to rules described below.
The actual golf game landscape with ever-changing playing field and fluctuating performance, means that the handicap determination can not be an exact science, but if the player tries to
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making the best score on each hole in all rounds
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to achieve so many counting score as possible per year
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to meet obligations in this system (applies very much also the club's committee members and green keepers)
We may nevertheless achieve a reasonably high degree of uniformity in handicap determination, and thereby obtain a sports fair handicap that shows the player's strength and allows players of varying strength to compete on an equal level.
Handicap is a single number with one decimal for the player's strength, measured by the number of strokes, he plays on an ideal course with Course Rating = Par and a Course Slope of 113 expressed with 1 decimal accuracy.
Playing Handicap (sHCP) is applied on the current course (set of tees) to be played, read on conversion table generated by a simple mathematical formula.
Playing Handicap (sHCP) is expressed in integers, for example, 7 strokes or 31 strokes, and the number of strokes over par, the player (if he obtains Stableford points on all holes) must play in order to play to his handicap, ie. get 36 Stableford points on chosen course.
EGA-handicap system in Latvia is used with permission from EGA:s Handicapping and Course Rating Committee.
EGA-Handicap System, Latvian edition, first of January 2010 on basis of LGF Course Rating and Sloping used with permission from the USGA.
This handicap system is in force in Latvia for handicap committees and members of Latvian golf clubs, members of LGF or associated clubs with LGFs central scoring and handicap system, golf admin.
§ 1 Latvian Golf Federation rights and obligations
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Latvian Golf Federation and has the supreme authority with regard to handicap system administration.
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Latvian Golf Federation has the right anytime to obtain information about handicap from member clubs.
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Latvian Golf Federation must approve all handicaps, to be set to scratch and plus handicap, immediately after setting.
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The Latvian Golf Federation is to establish conditions to be applied to counting tournaments and counting scores.
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Latvian Golf Federation has the authority to introduce and to use EDS (Extra Day Scores) for handicap regulation. EDS must follow the rules of EGA-handicap system.
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Latvian Golf Federation is to decide all disputes brought on the system.
Federation decisions made by Handicap and Course Rating Committee are final.
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Latvian Golf Federation to exclude clubs that do not follow rules of the system, from participating in open tournaments.
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Latvian Golf Federation must arrange Course Rating and Slope in accordance with the licence given by EGA.
§ 2 Member Clubs rights and obligations
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Member Club is a Latvian golf club, a member of the Latvian Golf Federation.
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The Member Club shall act as handicap authority to all members for whom they are home club, but subject to Latvian Golf Federation as the supreme authority.
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The Member Club shall ensure that club members are aware of the handicap system's rules and that the handicap system is used correctly and for every member club's players.
Meets member club not these requirements, the Latvian Golf Federation strip club member rights as handicap authority or implement the measures which the Latvian Golf Federation considers appropriate.
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Club Member must - among the members of the home club - designate a handicap committee to perform the duties described in § 3 at latest January 1st 2012.
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Member club must keep handicap register in LGFs central system of all home club players handicap influencing activities.
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The Member Club shall ensure that the courses surveys are approved by the Latvian Golf Federation and that the courses have been awarded the Course Rating and Slope of the Latvian Golf Federation.
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The Member Club shall have the maximum handicap apply to the players in handicap group 10, which has the club as home club.
§ 3 Handicap Committee (home club) rights and obligations
3.1. Handicap Committee must ensure that at a counting tournament at the club there is placed a list of participants' names. One of the tournament committee completed initial list will be such a participant list.
3.2. Handicap Committee must ensure (possibly in cooperation with the club's tournament committee) to the extent that it is possible that all score cards, which are delivered in a counting tournament and counting scores also (private scorer and EDS scores) returned to the handicap board, including incomplete led scorecard.
3.3. Handicap Committee must ensure that a list of members' current handicap is available on internet and/or on paper in the club house.
3.4. Handicap Committee shall, if a player has not done so, convert all scores to Stableford points and then proceed according to § 4.5 or § 4.7 of the player.
3.5. Handicap Committee must ensure that all changes in members' handicap immediately after an amendment is made, imposed on it under § 3.3 above handicap list.
3.6. Handicap Committee shall, on behalf of the players as they are at home club for the handicap register map to show the player's handicap issues (see § 2.5) with continuous registration of the player's counting scores immediately after delivery, and continually update the player's handicap to stabilize in chronological order.
3.7. Handicap Committee must ensure that suspended an EDS-start list (§ 8) with columns "Date", "Player", "Registered Number", "Handicap" and "Course tee". Handicap Committee must ensure that the rules of EDS compliance (§ 8) and that abuse of No Return does not take place (§ 4.6 and § 5).
3.8. Handicap Committee shall, as soon as the committee has set up a member's handicap to scratch (0.4 to +0.4) or plus handicap and annually thereafter, submit a copy of the player's handicap register map for approval by the Latvian Golf Federation. The reduction is valid immediately and became, in time, until the approval or non approval is available.
3.9. Handicap Committee shall have authority to suspend handicap, and the authority to regulate handicap.
3.10.Handicap Committee of a club that organizes a counting tournament, where the club is not a participating player's home club, ensure that scorecard with the counting scores sent to the player's home club.
If the club's computer system to conduct electronic handicap regulation can make the club record by scoring list, and the change is then transferred electronically to the player's home club. The player's score card to be stored for 2 months in the sponsoring club and possibly forwarded to the player's home club upon request.
3.11. Amended Handicap Committee must determine that a counting tournament would not apply as counting scores if fewer than 10% of participants scored the buffer zone or better. However, scores better than handicap registered and regulated in accordance with § 10 (See § 5.12.d)
3.12. Handicap Committee must approve all members’ handicaps and transfer of players starting handicap for every calendar year (Annual revision).
Players with handicap 4.4 and less who have not filed at least six counting scores in a calendar year, the year end have revised their handicap with an increase of 0.1 for each missing score up to six (maximum of up to four handicap, and have this handicap transferred as initial handicap for the new year. This also applies to professionals.
§ 4 The player's rights and obligations
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The player must choose one home club. If the player is a member of more than one member club, the player must give written notice to all clubs, in which clubs players are members, and the club has chosen as the home club. New (Note: If a player lives simultaneously in two countries in a period of three months the player can have home club in both countries.)
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The player must have only one handicap awarded the player and regulated by the home club.
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The player can only switch home club when given written notice of change to both the new and existing home club. Changing the home club has disabled regulatory immediate effect, while in other respects triggers a quarantine of three months in which the player can not play for his new or old home club in representative tournaments and matches.
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The player before participation in a counting tournament to ensure that the player's name on the attendance list (start list).
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The player is responsible for his handicap. Although home club performs service work on computerized registration and regulation of players' handicap, it is gaming's obligation and responsibility to know his exact current handicap (see § 10.10 and 10.11).
The player must always indicate Stableford points and together count them on one counting score. The player has the responsibility to follow changes in handicap and to know its exact current handicap.
Repeated or deliberate failure to give notice of counting scores (including No Return) and individuals will score better than handicap resulting suspension of handicap according to §
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Players must ensure that all scorecards from counting tournaments and EDS scores, letters "EDS" by the player returned to the TD whether they are completely filled out or not and ensure that individuals will score better than handicap filed for handicap committee in the home club.
Repeated or deliberate failure to give notice of counting scores (also No Return) and private scores better than handicap resulting suspension of handicap after § 11.
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The player must immediately give written notice to the handicap board in his home club for all counting scores (also No Return), obtained outside of the home club, including hcp> 4.5 too private to score better than handicap.
Repeated or deliberate omission of giving notice of counting tournament scores and private scores better than handicap acquired outside of the home club (also No Return) causes the suspension of handicap according to § 11.
For players with handicap <4.5, except that if the completed score card is not duly lodged at the home club within 14 days of a counting tournament abroad, and the player has a good reason not to have been able to obtain copies of result or copy of score card, the player's handicap is not suspended, but irreversibly increased by 0.1 per such round. Such scores do not count in the six scores, as mentioned in § 3.13.
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The player before the start of a counting tournament check his handicap on the tournament directors made start list and handed scorecard. If the above handicap is too high, it must be communicated to tournament directors along with the reason for the discrepancy. Handicap is therefore reduced to the correct.
If the above handicap is too low and the discrepancy is due to an incorrect or outdated information to the TD, the player must notify the tournament directors this and with its acceptance raise his handicap to correct.
If the inconsistency is because the player has been counting score to uplift, as handicap board (yet) have registered, the player can not without handicap board acceptance increase his handicap, but must accept it for the tournament too low handicap.
This approach is also used when the player participates in a non-counting tournament (eg. A match play tournament).
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Players (amateurs as well as pros) with 4.4 and less handicap shall provide a minimum six counting scores in a calendar year to avoid handicap uplift at annual revision according § 3.12. All other players must at annual revision have handicap approved and transferred to next year's season.
§ 5 Counting scores
5.1 "Handicap Conditions" are in games, Stableford or pair played with individual scores in tournaments as well as in private rounds better than handicap when the game is played under the following conditions:
• The course is subject to the national federation (members and slope rated by approval of national federation)
• The course is measured and the Course Rating (CR) and Slope, or (only in private sessions) track has SSS (Standard Scratch Score).
• A completed and signed a scorecard with marker signature.
• It is played with full handicaps.
• There are played golf rules and approved the Local Rules.
• Winter rule improvements on fairways can be introduced at max 1/3 of the counting holes in agreement with LGF.
A "counting score" is a score to be used for handicap adjustment after § 10 There are three kinds of counting scores:
A. A "counting tournament score" is any score (including No Return) from a "counting tournament" (see below) played under handicap conditions over 9 / 18 holes (see note *).
B. A "private counting score" is a score better than handicap, done in a private round of a player with a handicap greater than 4.5, and played under handicap conditions over 9 / 18 holes (see note *).
C. A "counting EDS score" is a score that played over 9 / 18 holes on the rules for EDS (Extra Day Scores) by a player with a handicap from 4.5 to 35.9 and handicap conditions. (See note *)
* Note: For handicap over 11.4 nine-hole rounds are acceptable, see § 05.11
A "score" is the numerical result hole for hole of a "round" of golf, and this score is one of the three above, it is called a "counting score".
A "counting tournament" is any tournament played under handicap conditions and organized by:
1st Latvian Golf Federation (LGF)
2nd Foreign Federation.
3rd Stroke plays tournaments in junior development in Latvia
4th A member club's tournament
5th A foreign club, a member of his country's national golf federation
6th Any tournament hosted by PGA (both PGA of Australia as any
State PGA) or a tour group.
In all Latvian Golf Federation organized tournaments (regardless of season) determines the Latvian Golf Federation Tournament Committee and the Handicap and CR-committee on handicap conditions are present, and whether there is a counting tournament with a counting score.
"No Return" in a counting tournament will say that the player does not finish the round, but players must still submit his scorecard to the tournament directors unless reasonable cause is (acute illness, etc.). Lack of a written score card is a breach of the Handicap System, see § 4.6.
5.2 The club shall undertake all scores counting on the player's handicap card electronically.
5.3 Any score better than handicap by not counting tournaments with handicap conditions is a counting score, which, after conversion into Stableford must be submitted by the player to regulation according to § 10 - this is only applicable to players with handicaps higher than 4.5, and can only used to adjust the handicap of 4.5 is reached downward.
5.4 Any score better than handicap from private sessions with handicap conditions, including private match play matches, which is put out, is a counting score, which, after conversion to the Stableford must be submitted by the player after § 10. This is only valid for a player with handicaps higher than 4.5, and can only be used to adjust the handicap of 4.5 is reached downward.
5.5 A score better than handicap, lodged by a void wave in a counting tournament or a round in which handicap committee in accordance with § 3.12, has specified that the round should not be a counting tournament, is a counting score.
5.7 A score from a counting round of a game of one reason or another has been disqualified, is a counting score, except if
• the player using illegal clubs (Rule 4-1, 4-2 and 4-3)
• the player use more than one caddy simultaneously (Rule 6-4)
• player has been practicing on the course before a tournament (Rule 7-1)
• player uses artificial aids, etc. (Rule 14-3)
• player plays from the wrong place (Rule 20-7).
• players have agreed to override Golf Rules (Rule 1-3)
• Note: Played a private match (or tournament) along with a counting tournament, then the rule breaks in the counting tournament, which will be permitted in the private match, does not preclude the use of the private round for hcp lowering.
• These scores may possibly be used by handicap committee as a basis for discretionary regulation.
5.8 A score better than handicap in a tournament where the permitted number of clubs is less than 14 (eg. Three-club tournament) is a counting score.
5.9 Individual scores and No Return from one four ball aggregate tournament plus scores better than handicap (which must be greater than 4.5) from rounds in which participants play as a partner with another participant, the numerator scorer. However, see 5.12 k.
5.10 Scores from a course with make shift course conditions are counting scores, if the Latvian Golf Federation has approved it.
5.11 Changed for Groups 3-5 with handicap over 11.4 shall take the score over nine holes in Stableford score for nine holes plus 18 Stableford points.
5.12 The following scores are never counting scores:
a. If the runway length discrepancy of more than 100 meters from the measured path, or if more than two provisional greens (nine holes, however, more than one green).
b. If winter rule improvements are permitted outside the fairway.
c. If there is winter rule improvement on fairway - unless the Latvian Golf Federation has approved it.
d. Scores from rounds are not played after the Golf Rules or Latvian Golf Federation approved Local Rules. Example: Hole cups greater than 108 mm in diameter, Scores from rounds worse than handicap, where holes are not played in the order determined by the Committee.
e. Scores worse than handicap from all tournaments in which participants play as a partner to another participant - with the exception of four ball aggregate tournaments and other tournaments where scores are added together.
f. Scores worse than handicap from a cancelled round or a round of handicap committee has declared not count under § 3.12.
g. Scores achieved by amateurs in a PRO-AM, because of the possibility of "professional" advice. But the tournament is organized by the PGA or counting to PGAs ranking, is the counting for the pro.
h. Scores worse than handicap from Stableford and couples tournaments (see § 5 and § 7.4), which provide less than full handicap.
i. Scores worse than handicap in a tournament where the permitted number of clubs is less than the 14th
Note: All these are not counting scores (5.12 al) can naturally be used by Handicap Committee as a basis for discretionary adjustment pursuant to § 13
§ 6 Playing Handicap (sHCP)
6.1 In stroke play, par and Stableford competitions the player gets extra strokes (handicap) compared to Par of the course from a conversion table (slope table) corresponding to tee ground for the round.
6.2 Handicap on the other side of 0 (very talented players) are called "plus handicap" which means that such player has to play better than course Par.
6.3 The playing handicap player receives at the set of tees on a golf course is in the conversion tables derived from the player's handicap by the following formula:
Playing Handicap (sHCP) = Exact Handicap (eHCP) x (Slope Rating / 113) + (Course Rating (CR) - Par)
eHCP is given with one decimal accuracy except in handicap group 10 which is integer and reduce only. If the eHCP is a plus handicap, it as a negative value in the formula, and if the formula gives a negative handicap, it should be interpreted as a plus handicap.
Slope is given to all tees, with different colours or distance marks, which imply that there are several courses in a golf course, and depending on gender and tee placement.
Course Rating given to one decimal place and generally speaking the length difference of 20 meters gives approximately 0,1 change in CR. It is important that the courses are set up in accordance with the sloping data. Green keepers should therefore not change the total distances more than 60 meters due to moving tee marks. If one hole is made shorter it should be compensated by making other holes longer and vice versa.
Par is an integer and normally set after length of the hole or the natural playing way for each hole.
Playing Handicap is an integer and the extra strokes compared to Par of the course are distributed to each hole in accordance with hole’s index. Hole index is a series of numbers applied to the course over 18 holes. If a course has less than 18 holes and a game is played over 18 holes the hole can get a second or third index which is to be used when the hole is played second or third time on the same round. All handicaps are set over 18 holes.
6.4 Distribution of strokes with applying index over 18 holes is in table appendix.
§ 7 Stableford
7.1 Before handicap regulating the player must convert the counting scores to Stableford points.
7.2 Application of Stableford points is to reduce the importance of an exceptionally high score on a hole, since such a score does not reflect the player's true playing potential.
7.3 The handicap-related purposes is Stableford points awarded in relation to the hole par which is calculated for each player as course par plus handicap strokes distributed according to hole index
Individual par (iPar) calculated as Course Par plus distributed handicap strokes
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Net Score
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Stbf points
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Called
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No score
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0
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Stripe
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2 or more over iPar
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0
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Net double bogey
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1 over iPar
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1
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Net bogey
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iPar
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2
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Net par
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1 better than iPar
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3
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Net birdie
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2 better than iPar
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4
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Net eagle
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3 better than iPar
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5
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Net albatross
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4 better than iPar
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6
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No name
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§ 8 Extra Day Scores (EDS)
8.1 An Extra Day Scores are all scores converted to Stableford points game after the rules for EDS and handicap conditions.
8.2 EDS is only valid for players in the handicap groups 2, 3, 4 and 5
8.3 EDS can only be played on the player's home club course and has been introduced to secure the possibilities of getting an active handicap under EGA s rules of minimum rounds per year for handicap setting. (Home club can be more than one if it is in two different countries).
8.4 The player decide when he/she will play an EDS score. After an EDS score the player can not play EDS the next six days. A player can make maximum 5 EDS scores per year. EDS scores can be played all year, when handicap conditions are met.
8.5 To EDS is a counting score (9 or 18 holes according to hcp group) the player before the round, but the same day, writing on an EDS start list with the following information:
a. Date
b. The player's name and membership number
c. The player's handicap
d. The marker's name
* Note: If the marker is fully aware of the relationship before tee off, it is accepted that the first write pointer in the list immediately after the game. He writes thus also that he was aware of its obligation even before the start. This relief does not apply to the player.
8.6 The player after the round lodge a completed and signed (including marker) scorecard marked "EDS" with scores converted to Stableford points.
8.7 "No Return" in EDS will say that the player has interrupted the game and deliver a scorecard marked "No Return" and "EDS" and is able to give a good reason to interrupt the game. Misuse of "No Return" in EDS may lead to board suspension of the player and the cursor handicaps.
8.8 A player can not play to a handicap of 4.5 or over 36 using EDS.
§ 9 Acquisition of the first handicap
9.1 Only members of a club member can receive a handicap and only by his home club.
9.2 In order to acquire his first handicap in group 10, it is sufficient that a player has been passing a green card course approved or has proven ability from other golf federation as golfer. A player should return score card in order for handicap committee to set appropriate handicap. If the club assigns handicaps over 36, the player can participate in competitions and is given sHCP in accordance with the rules of the competition which in case not stated in the competitions rules is maximum 36,0 eHCP.
If the player scores better than actual handicap during such a round the new handicap is estimated on basis of Stableford points calculated on eHCP but for the tournament placed with the sHCP as count.
9.3 In order to acquire his first handicap in handicap groups 1, 2, 3, 4 or 5, a player who does not already have a handicap in group ten, mail three Stableford score card from three 18-hole rounds played on home ground under handicap conditions. Number of strokes are awarded after conversion table corresponding to 36 handicap, and one of scores must be on 36 points or better.
Scorecard must be led and signed by the marker and signed by the player.
These rounds will usually be private sessions or start tournaments as you can not participate in other tournaments without disabilities.
Is the best score equal to x Stableford points, achieved the following:
New Handicap = 36 - (113 (x - 36) / Slope) and the result rounded to whole numbers.
Example: A player who must acquire or reacquire his handicap is sent out to play three rounds with handicap 36. He gets with these handicap 38 strokes assigned to the course, which has Slope 129. He scored respectively 45, 47 and 39 points. Best is the 47th His new handicap is calculated as follows:
X - 36 = 47-36 = 11
11 multiplied by 113 is 1243
1243/Slope = 1243/129 = 9.64
36 to 9.64 = 26.36 which is rounded to 26
Player will be given handicap 26.
There can not be acquired first handicap in handicap group 1 without written permission from the Latvian Golf Federation.
9.4 Handicap Committee may assign a player a first handicap, which is lower than what the player should have according to § 9.2 and § 9.3, whose handicap committee has reason to believe that a lower handicap corresponds better to the player's current playing strength.
9.5 If a player can not achieve a score that correspond to a handicap similar to the home club's maximum handicap, the home club's handicap committee award the player a handicap equal to the home club's maximum handicap.
9.6 Once a player so acquired its first handicap, this can only be changed by the application of regulatory rules in § 10 or at the discretion of the paragraph § 13 which is medical reasons or annual review.
§ 10 Setting of handicap
10.1 Based on result from counting rounds of golf the following table shows the changes that should be done for different handicap groups. LGF has chosen to call the hcp group 37-54 group 10 as help to know how many strokes change different results give in each hcp group when playing better than sHCP. It is 10% of the value of category value.
Changes in eHCP based on Stableford points
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Player
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Changes in eHCP
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Category
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eHCP
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Stbf point
over 36
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Stbf lower than
buffer zone
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1
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- 4,4
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-0,1/point
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+0,1
|
|
2
|
4,5-11,4
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-0,2/point
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+0,1
|
|
3
|
11,5-18,4
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-0,3/point
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+0,1
|
|
4
|
18,5-26,4
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-0,4/point
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+0,2
|
|
5
|
26,5-36,0
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-0,5/point
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+0,2
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|
10
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37-54
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-1/point
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0
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10.2 The table below shows the handicap changes according to type of changes and what is possible in different handicap groups.
Changes in eHCP based on player category
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Player
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Buffer zone Stbf points
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Type of change
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Category
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eHCP
|
18-hole score
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9-hole score
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Reduce only (social game)
|
Compet-
ition
|
EDS
|
|
1
|
- 4,4
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35-36
|
n.a.
|
n.a.
|
yes
|
n.a.
|
|
2
|
4,5-11,4
|
34-36
|
n.a.
|
yes
|
yes
|
Max 5/year
|
|
3
|
11,5-18,4
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33-36
|
yes
|
yes
|
yes
|
Max 5/year
|
|
4
|
18,5-26,4
|
32-36
|
yes
|
yes
|
yes
|
Max 5/year
|
|
5
|
26,5-36,0
|
31-36
|
yes
|
yes
|
yes
|
Max 5/year
|
|
10
|
37-54
|
36
|
yes
|
yes
|
yes
|
Max 5/year
|
Distributed handicap strokes given for 2 Stableford points
|
Hole index
|
1
|
2
|
3
|
4
|
5
|
6
|
7
|
8
|
9
|
10
|
11
|
12
|
13
|
14
|
15
|
16
|
17
|
18
|
|
sHCP
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
plus 4
|
0
|
0
|
0
|
0
|
0
|
0
|
0
|
0
|
0
|
0
|
0
|
0
|
0
|
0
|
-1
|
-1
|
-1
|
-1
|
|
plus 3
|
0
|
0
|
0
|
0
|
0
|
0
|
0
|
0
|
0
|
0
|
0
|
0
|
0
|
0
|
0
|
-1
|
-1
|
-1
|
|
plus 2
|
0
|
0
|
0
|
0
|
0
|
0
|
0
|
0
|
0
|
0
|
0
|
0
|
0
|
0
|
0
|
0
|
-1
|
-1
|
|
plus 1
|
0
|
0
|
0
|
0
|
0
|
0
|
0
|
0
|
0
|
0
|
0
|
0
|
0
|
0
|
0
|
0
|
0
|
-1
|
|
0
|
0
|
0
|
0
|
0
|
0
|
0
|
0
|
0
|
0
|
0
|
0
|
0
|
0
|
0
|
0
|
0
|
0
|
0
|
|
1
|
1
|
0
|
0
|
0
|
0
|
0
|
0
|
0
|
0
|
0
|
0
|
0
|
0
|
0
|
0
|
0
|
0
|
0
|
|
2
|
1
|
1
|
0
|
0
|
0
|
0
|
0
|
0
|
0
|
0
|
0
|
0
|
0
|
0
|
0
|
0
|
0
|
0
|
|
3
|
1
|
1
|
1
|
0
|
0
|
0
|
0
|
0
|
0
|
0
|
0
|
0
|
0
|
0
|
0
|
0
|
0
|
0
|
|
4
|
1
|
1
|
1
|
1
|
0
|
0
|
0
|
0
|
0
|
0
|
0
|
0
|
0
|
0
|
0
|
0
|
0
|
0
|
|
5
|
1
|
1
|
1
|
1
|
1
|
0
|
0
|
0
|
0
|
0
|
0
|
0
|
0
|
0
|
0
|
0
|
0
|
0
|
|
6
|
1
|
1
|
1
|
1
|
1
|
1
|
0
|
0
|
0
|
0
|
0
|
0
|
0
|
0
|
0
|
0
|
0
|
0
|
|
7
|
1
|
1
|
1
|
1
|
1
|
1
|
1
|
0
|
0
|
0
|
0
|
0
|
0
|
0
|
0
|
0
|
0
|
0
|
|
8
|
1
|
1
|
1
|
1
|
1
|
1
|
1
|
1
|
0
|
0
|
0
|
0
|
0
|
0
|
0
|
0
|
0
|
0
|
|
9
|
1
|
1
|
1
|
1
|
1
|
1
|
1
|
1
|
1
|
0
|
0
|
0
|
0
|
0
|
0
|
0
|
0
|
0
|
|
10
|
1
|
1
|
1
|
1
|
1
|
1
|
1
|
1
|
1
|
1
|
0
|
0
|
0
|
0
|
0
|
0
|
0
|
0
|
|
11
|
1
|
1
|
1
|
1
|
1
|
1
|
1
|
1
|
1
|
1
|
1
|
0
|
0
|
0
|
0
|
0
|
0
|
0
|
|
12
|
1
|
1
|
1
|
1
|
1
|
1
|
1
|
1
|
1
|
1
|
1
|
1
|
0
|
0
|
0
|
0
|
0
|
0
|
|
13
|
1
|
1
|
1
|
1
|
1
|
1
|
1
|
1
|
1
|
1
|
1
|
1
|
1
|
0
|
0
|
0
|
0
|
0
|
|
14
|
1
|
1
|
1
|
1
|
1
|
1
|
1
|
1
|
1
|
1
|
1
|
1
|
1
|
1
|
0
|
0
|
0
|
0
|
|
15
|
1
|
1
|
1
|
1
|
1
|
1
|
1
|
1
|
1
|
1
|
1
|
1
|
1
|
1
|
1
|
0
|
0
|
0
|
|
16
|
1
|
1
|
1
|
1
|
1
|
1
|
1
|
1
|
1
|
1
|
1
|
1
|
1
|
1
|
1
|
1
|
0
|
0
|
|
17
|
1
|
1
|
1
|
1
|
1
|
1
|
1
|
1
|
1
|
1
|
1
|
1
|
1
|
1
|
1
|
1
|
1
|
0
|
|
18
|
1
|
1
|
1
|
1
|
1
|
1
|
1
|
1
|
1
|
1
|
1
|
1
|
1
|
1
|
1
|
1
|
1
|
1
|
|
19
|
2
|
1
|
1
|
1
|
1
|
1
|
1
|
1
|
1
|
1
|
1
|
1
|
1
|
1
|
1
|
1
|
1
|
1
|
|
20
|
2
|
2
|
1
|
1
|
1
|
1
|
1
|
1
|
1
|
1
|
1
|
1
|
1
|
1
|
1
|
1
|
1
|
1
|
|
21
|
2
|
2
|
2
|
1
|
1
|
1
|
1
|
1
|
1
|
1
|
1
|
1
|
1
|
1
|
1
|
1
|
1
|
1
|
|
22
|
2
|
2
|
2
|
2
|
1
|
1
|
1
|
1
|
1
|
1
|
1
|
1
|
1
|
1
|
1
|
1
|
1
|
1
|
|
23
|
2
|
2
|
2
|
2
|
2
|
1
|
1
|
1
|
1
|
1
|
1
|
1
|
1
|
1
|
1
|
1
|
1
|
1
|
|
24
|
2
|
2
|
2
|
2
|
2
|
2
|
1
|
1
|
1
|
1
|
1
|
1
|
1
|
1
|
1
|
1
|
1
|
1
|
|
25
|
2
|
2
|
2
|
2
|
2
|
2
|
2
|
1
|
1
|
1
|
1
|
1
|
1
|
1
|
1
|
1
|
1
|
1
|
|
26
|
2
|
2
|
2
|
2
|
2
|
2
|
2
|
2
|
1
|
1
|
1
|
1
|
1
|
1
|
1
|
1
|
1
|
1
|
|
27
|
2
|
2
|
2
|
2
|
2
|
2
|
2
|
2
|
2
|
1
|
1
|
1
|
1
|
1
|
1
|
1
|
1
|
1
|
|
28
|
2
|
2
|
2
|
2
|
2
|
2
|
2
|
2
|
2
|
2
|
1
|
1
|
1
|
1
|
1
|
1
|
1
|
1
|
|
29
|
2
|
2
|
2
|
2
|
2
|
2
|
2
|
2
|
2
|
2
|
2
|
1
|
1
|
1
|
1
|
1
|
1
|
1
|
|
30
|
2
|
2
|
2
|
2
|
2
|
2
|
2
|
2
|
2
|
2
|
2
|
2
|
1
|
1
|
1
|
1
|
1
|
1
|
|
31
|
2
|
2
|
2
|
2
|
2
|
2
|
2
|
2
|
2
|
2
|
2
|
2
|
2
|
1
|
1
|
1
|
1
|
1
|
|
32
|
2
|
2
|
2
|
2
|
2
|
2
|
2
|
2
|
2
|
2
|
2
|
2
|
2
|
2
|
1
|
1
|
1
|
1
|
|
33
|
2
|
2
|
2
|
2
|
2
|
2
|
2
|
2
|
2
|
2
|
2
|
2
|
2
|
2
|
2
|
1
|
1
|
1
|
|
34
|
2
|
2
|
2
|
2
|
2
|
2
|
2
|
2
|
2
|
2
|
2
|
2
|
2
|
2
|
2
|
2
|
1
|
1
|
|
35
|
2
|
2
|
2
|
2
|
2
|
2
|
2
|
2
|
2
|
2
|
2
|
2
|
2
|
2
|
2
|
2
|
2
|
1
|
|
36
|
2
|
2
|
2
|
2
|
2
|
2
|
2
|
2
|
2
|
2
|
2
|
2
|
2
|
2
|
2
|
2
|
2
|
2
|
|
37
|
3
|
2
|
2
|
2
|
2
|
2
|
2
|
2
|
2
|
2
|
2
|
2
|
2
|
2
|
2
|
2
|
2
|
2
|
|
38
|
3
|
3
|
2
|
2
|
2
|
2
|
2
|
2
|
2
|
2
|
2
|
2
|
2
|
2
|
2
|
2
|
2
|
2
|
|
39
|
3
|
3
|
3
|
2
|
2
|
2
|
2
|
2
|
2
|
2
|
2
|
2
|
2
|
2
|
2
|
2
|
2
|
2
|
|
40
|
3
|
3
|
3
|
3
|
2
|
2
|
2
|
2
|
2
|
2
|
2
|
2
|
2
|
2
|
2
|
2
|
2
|
2
|
|
41
|
3
|
3
|
3
|
3
|
3
|
2
|
2
|
2
|
2
|
2
|
2
|
2
|
2
|
2
|
2
|
2
|
2
|
2
|
|
42
|
3
|
3
|
3
|
3
|
3
|
3
|
2
|
2
|
2
|
2
|
2
|
2
|
2
|
2
|
2
|
2
|
2
|
2
|
|
43
|
3
|
3
|
3
|
3
|
3
|
3
|
3
|
2
|
2
|
2
|
2
|
2
|
2
|
2
|
2
|
2
|
2
|
2
|
|
44
|
3
|
3
|
3
|
3
|
3
|
3
|
3
|
3
|
2
|
2
|
2
|
2
|
2
|
2
|
2
|
2
|
2
|
2
|
|
45
|
3
|
3
|
3
|
3
|
3
|
3
|
3
|
3
|
3
|
2
|
2
|
2
|
2
|
2
|
2
|
2
|
2
|
2
|
|
46
|
3
|
3
|
3
|
3
|
3
|
3
|
3
|
3
|
3
|
3
|
2
|
2
|
2
|
2
|
2
|
2
|
2
|
2
|
|
47
|
3
|
3
|
3
|
3
|
3
|
3
|
3
|
3
|
3
|
3
|
3
|
2
|
2
|
2
|
2
|
2
|
2
|
2
|
|
48
|
3
|
3
|
3
|
3
|
3
|
3
|
3
|
3
|
3
|
3
|
3
|
3
|
2
|
2
|
2
|
2
|
2
|
2
|
|
49
|
3
|
3
|
3
|
3
|
3
|
3
|
3
|
3
|
3
|
3
|
3
|
3
|
3
|
2
|
2
|
2
|
2
|
2
|
|
50
|
3
|
3
|
3
|
3
|
3
|
3
|
3
|
3
|
3
|
3
|
3
|
3
|
3
|
3
|
2
|
2
|
2
|
2
|
|
51
|
3
|
3
|
3
|
3
|
3
|
3
|
3
|
3
|
3
|
3
|
3
|
3
|
3
|
3
|
3
|
2
|
2
|
2
|
|
52
|
3
|
3
|
3
|
3
|
3
|
3
|
3
|
3
|
3
|
3
|
3
|
3
|
3
|
3
|
3
|
3
|
2
|
2
|
|
53
|
3
|
3
|
3
|
3
|
3
|
3
|
3
|
3
|
3
|
3
|
3
|
3
|
3
|
3
|
3
|
3
|
3
|
2
|
|
54
|
3
|
3
|
3
|
3
|
3
|
3
|
3
|
3
|
3
|
3
|
3
|
3
|
3
|
3
|
3
|
3
|
3
|
3
|
|
55
|
4
|
3
|
3
|
3
|
3
|
3
|
3
|
3
|
3
|
3
|
3
|
3
|
3
|
3
|
3
|
3
|
3
|
3
|
|
56
|
4
|
4
|
3
|
3
|
3
|
3
|
3
|
3
|
3
|
3
|
3
|
3
|
3
|
3
|
3
|
3
|
3
|
3
|
|
57
|
4
|
4
|
4
|
3
|
3
|
3
|
3
|
3
|
3
|
3
|
3
|
3
|
3
|
3
|
3
|
3
|
3
|
3
|
|
58
|
4
|
4
|
4
|
4
|
3
|
3
|
3
|
3
|
3
|
3
|
3
|
3
|
3
|
3
|
3
|
3
|
3
|
3
|
|
59
|
4
|
4
|
4
|
4
|
4
|
3
|
3
|
3
|
3
|
3
|
3
|
3
|
3
|
3
|
3
|
3
|
3
|
3
|
|
60
|
4
|
4
|
4
|
4
|
4
|
4
|
3
|
3
|
3
|
3
|
3
|
3
|
3
|
3
|
3
|
3
|
3
|
3
|
|
61
|
4
|
4
|
4
|
4
|
4
|
4
|
4
|
3
|
3
|
3
|
3
|
3
|
3
|
3
|
3
|
3
|
3
|
3
|
|
62
|
4
|
4
|
4
|
4
|
4
|
4
|
4
|
4
|
3
|
3
|
3
|
3
|
3
|
3
|
3
|
3
|
3
|
3
|