197 lines
7.0 KiB
Markdown
197 lines
7.0 KiB
Markdown
---
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title: Deal cards for FreeCell
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id: 59694356a6e7011f7f1c5f4e
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challengeType: 5
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---
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## Description
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<section id='description'>
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<i>FreeCell</i> is the solitaire card game that Paul Alfille introduced to the PLATO system in 1978. Jim Horne, at Microsoft, changed the name to FreeCell and reimplemented the game for <a href="http://rosettacode.org/wiki/DOS" title="DOS">DOS</a>, then <a href="http://rosettacode.org/wiki/Windows" title="Windows">Windows</a>. This version introduced 32000 numbered deals. (The <a href="http://www.solitairelaboratory.com/fcfaq.html" title="link: http://www.solitairelaboratory.com/fcfaq.html">FreeCell FAQ</a> tells this history.)
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As the game became popular, Jim Horne disclosed <a href="http://www.solitairelaboratory.com/mshuffle.txt" title="link: http://www.solitairelaboratory.com/mshuffle.txt">the algorithm</a>, and other implementations of FreeCell began to reproduce the Microsoft deals. These deals are numbered from 1 to 32000. Newer versions from Microsoft have 1 million deals, numbered from 1 to 1000000; some implementations allow numbers outside that range.
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The algorithm uses this <a href="http://rosettacode.org/wiki/linear congruential generator" title="linear congruential generator">linear congruential generator</a> from Microsoft C:
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<ul>
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<li>$state_{n + 1} \equiv 214013 \times state_n + 2531011 \pmod{2^{31}}$</li>
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<li>$rand_n = state_n \div 2^{16}$</li>
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<li>$rand_n$ is in range 0 to 32767.</li>
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</ul>
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The algorithm follows:
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<ol>
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<li>Seed the RNG with the number of the deal.
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<li>Create an <a href="http://rosettacode.org/wiki/array" title="array">array</a> of 52 cards: Ace of Clubs, Ace of Diamonds, Ace of Hearts, Ace of Spades, 2 of Clubs, 2 of Diamonds, and so on through the ranks: Ace, 2, 3, 4, 5, 6, 7, 8, 9, 10, Jack, Queen, King. The array indexes are 0 to 51, with Ace of Clubs at 0, and King of Spades at 51.</li>
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<li>Until the array is empty:</li>
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<li>Choose a random card at index ≡ next random number (mod array length).</li>
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<ul>
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<li>Swap this random card with the last card of the array.</li>
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<li>Remove this random card from the array. (Array length goes down by 1.)</li>
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<li>Deal this random card.</li>
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</ul>
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<li>Deal all 52 cards, face up, across 8 columns. The first 8 cards go in 8 columns, the next 8 cards go on the first 8 cards, and so on.</li>
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</ol>
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<b>Example:</b>
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<b>Order to deal cards</b>
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<pre> 1 2 3 4 5 6 7 8
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9 10 11 12 13 14 15 16
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17 18 19 20 21 22 23 24
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25 26 27 28 29 30 31 32
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33 34 35 36 37 38 39 40
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41 42 43 44 45 46 47 48
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49 50 51 52</pre>
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<b>Game #1</b>
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<pre>[
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['JD', '2D', '9H', 'JC', '5D', '7H', '7C', '5H'],
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['KD', 'KC', '9S', '5S', 'AD', 'QC', 'KH', '3H'],
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['2S', 'KS', '9D', 'QD', 'JS', 'AS', 'AH', '3C'],
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['4C', '5C', 'TS', 'QH', '4H', 'AC', '4D', '7S'],
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['3S', 'TD', '4S', 'TH', '8H', '2C', 'JH', '7D'],
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['6D', '8S', '8D', 'QS', '6C', '3D', '8C', 'TC'],
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['6S', '9C', '2H', '6H']
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]</pre>
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<b>Game #617</b>
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<pre>[
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['7D', 'AD', '5C', '3S', '5S', '8C', '2D', 'AH'],
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['TD', '7S', 'QD', 'AC', '6D', '8H', 'AS', 'KH'],
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['TH', 'QC', '3H', '9D', '6S', '8D', '3D', 'TC'],
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['KD', '5H', '9S', '3C', '8S', '7H', '4D', 'JS'],
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['4C', 'QS', '9C', '9H', '7C', '6H', '2C', '2S'],
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['4S', 'TS', '2H', '5D', 'JC', '6C', 'JH', 'QH'],
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['JD', 'KS', 'KC', '4H']
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]</pre>
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Write a function to take a deal number and deal cards in the same order as this algorithm. The function must return a two dimensional array representing the FreeCell board.
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Deals can also be checked against <a href="http://freecellgamesolutions.com/" title="link: http://freecellgamesolutions.com/">FreeCell solutions to 1000000 games</a>. (Summon a video solution, and it displays the initial deal.)
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</section>
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## Instructions
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<section id='instructions'>
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</section>
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## Tests
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<section id='tests'>
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```yml
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tests:
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- text: <code>dealFreeCell</code> is a function.
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testString: assert(typeof dealFreeCell === 'function', '<code>dealFreeCell</code> is a function.');
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- text: <code>dealFreeCell(seed)</code> should return an object.
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testString: assert(typeof dealFreeCell(1) === 'object', '<code>dealFreeCell(seed)</code> should return an object.');
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- text: <code>dealFreeCell(seed)</code> should return an array of length 7.
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testString: assert(dealFreeCell(1).length === 7, '<code>dealFreeCell(seed)</code> should return an array of length 7.');
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- text: "<code>dealFreeCell(1)</code> should return an array identical to example \"Game #1\""
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testString: "assert.deepEqual(dealFreeCell(1), game1, '<code>dealFreeCell(1)</code> should return an array identical to example \"Game #1\"');"
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- text: "<code>dealFreeCell(617)</code> should return an array identical to example \"Game #617\""
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testString: "assert.deepEqual(dealFreeCell(617), game617, '<code>dealFreeCell(617)</code> should return an array identical to example \"Game #617\"');"
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```
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</section>
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## Challenge Seed
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<section id='challengeSeed'>
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<div id='js-seed'>
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```js
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function dealFreeCell (seed) {
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// Good luck!
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return true;
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}
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```
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</div>
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### After Test
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<div id='js-teardown'>
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```js
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const replaceThis = 3;
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const game1 = [
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['JD', '2D', '9H', 'JC', '5D', '7H', '7C', '5H'],
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['KD', 'KC', '9S', '5S', 'AD', 'QC', 'KH', '3H'],
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['2S', 'KS', '9D', 'QD', 'JS', 'AS', 'AH', '3C'],
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['4C', '5C', 'TS', 'QH', '4H', 'AC', '4D', '7S'],
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['3S', 'TD', '4S', 'TH', '8H', '2C', 'JH', '7D'],
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['6D', '8S', '8D', 'QS', '6C', '3D', '8C', 'TC'],
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['6S', '9C', '2H', '6H']
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];
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const game617 = [
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['7D', 'AD', '5C', '3S', '5S', '8C', '2D', 'AH'],
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['TD', '7S', 'QD', 'AC', '6D', '8H', 'AS', 'KH'],
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['TH', 'QC', '3H', '9D', '6S', '8D', '3D', 'TC'],
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['KD', '5H', '9S', '3C', '8S', '7H', '4D', 'JS'],
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['4C', 'QS', '9C', '9H', '7C', '6H', '2C', '2S'],
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['4S', 'TS', '2H', '5D', 'JC', '6C', 'JH', 'QH'],
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['JD', 'KS', 'KC', '4H']
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];
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```
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</div>
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</section>
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## Solution
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<section id='solution'>
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```js
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// RNG
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function FreeCellRNG (seed) {
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return {
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lastNum: seed,
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next() {
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this.lastNum = ((214013 * this.lastNum) + 2531011) % (Math.pow(2, 31));
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return this.lastNum >> 16;
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}
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};
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}
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// Get cards
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function getDeck() {
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const ranks = ['A', '2', '3', '4', '5', '6', '7', '8', '9', 'T', 'J', 'Q', 'K'];
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const suits = ['C', 'D', 'H', 'S'];
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const cards = [];
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for (let i = 0; i < ranks.length; i += 1) {
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for (let j = 0; j < suits.length; j += 1) {
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cards.push(`${ranks[i]}${suits[j]}`);
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}
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}
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return cards;
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}
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function dealFreeCell(seed) {
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const rng = FreeCellRNG(seed);
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const deck = getDeck();
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const deltCards = [[], [], [], [], [], [], []];
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let currentColumn = 0;
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let currentRow = 0;
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let rand;
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let temp;
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let card;
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while (deck.length > 0) {
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// Choose a random card
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rand = rng.next() % deck.length;
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// Swap this random card with the last card in the array
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temp = deck[deck.length - 1];
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deck[deck.length - 1] = deck[rand];
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deck[rand] = temp;
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// Remove this card from the array
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card = deck.pop();
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// Deal this card
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deltCards[currentRow].push(card);
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currentColumn += 1;
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if (currentColumn === 8) {
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currentColumn = 0;
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currentRow += 1;
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}
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}
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return deltCards;
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}
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```
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</section>
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