function printHeap(heap, index, level) {
    if (index >= heap.length) {
        return;
    }
    console.log("  ".repeat(level) + heap[index]);
    printHeap(heap, 2 * index + 1, level + 1);
    printHeap(heap, 2 * index + 2, level + 1);
}

//You can call this function by passing in the heap array and the index of the root node, which is typically 0, and level = 0.

let heap = [3, 8, 7, 15, 17, 30, 35, 2, 4, 5, 9];
printHeap(heap,0,0)

const toFixed = (n, fixed) => ~~(Math.pow(10, fixed) * n) / Math.pow(10, fixed);
// Examples
toFixed(25.198726354, 1);       // 25.1
toFixed(25.198726354, 2);       // 25.19
toFixed(25.198726354, 3);       // 25.198
toFixed(25.198726354, 4);       // 25.1987
toFixed(25.198726354, 5);       // 25.19872
toFixed(25.198726354, 6);       // 25.198726

const euclideanDistance = (a, b) =>
  Math.hypot(...Object.keys(a).map(k => b[k] - a[k]));
  
euclideanDistance([1, 1], [2, 3]); // ~2.2361
euclideanDistance([1, 1, 1], [2, 3, 2]); // ~2.4495

const Discord = require('discord.js');
const client = new Discord.Client();
const token = 'YOUR_BOT_TOKEN';

// When the bot is ready, log a message to the console
client.on('ready', () => {
  console.log(`Logged in as ${client.user.tag}!`);
});

// When a user sends a message, check if they are authenticated
client.on('message', async (msg) => {
  if (!msg.author.bot && !msg.author.authenticated) {
    const filter = (m) => m.author.id === msg.author.id;
    const collector = msg.channel.createMessageCollector(filter, { time: 15000 });

    // Send an authentication message to the user
    msg.author.send('Please authenticate yourself by clicking this link: ' + generateAuthURL(msg.author.id));

    collector.on('collect', async (m) => {
      // Check if the message contains the authentication code
      if (m.content.startsWith('!auth ')) {
        const code = m.content.slice(6);
        const { access_token } = await getAccessToken(code);

        // Set the user's authenticated status and access token
        msg.author.authenticated = true;
        msg.author.access_token = access_token;
        collector.stop();
      }
    });

    collector.on('end', () => {
      if (!msg.author.authenticated) {
        msg.author.send('Authentication timed out.');
      }
    });
  }
});

// Generate an authentication URL for the user
function generateAuthURL(userId) {
  const redirectURI = encodeURIComponent('YOUR_REDIRECT_URL');
  const scopes = 'identify';
  const clientID = 'YOUR_CLIENT_ID';

  return `https://discord.com/api/oauth2/authorize?client_id=${clientID}&redirect_uri=${redirectURI}&response_type=code&scope=${scopes}&state=${userId}`;
}

// Exchange the authorization code for an access token
async function getAccessToken(code) {
  const redirectURI = encodeURIComponent('YOUR_REDIRECT_URL');
  const clientID = 'YOUR_CLIENT_ID';
  const clientSecret = 'YOUR_CLIENT_SECRET';

  const res = await fetch('https://discord.com/api/oauth2/token', {
    method: 'POST',
    headers: {
      'Content-Type': 'application/x-www-form-urlencoded',
    },
    body: `grant_type=authorization_code&code=${code}&redirect_uri=${redirectURI}&client_id=${clientID}&client_secret=${clientSecret}`,
  });

  return await res.json();
}

client.login(token);

const union = (...arr) => [...new Set(arr.flat())];

// Example
union([1, 2], [2, 3], [3]);     // [1, 2, 3]

const levenshteinDistance = (s, t) => {
  if (!s.length) return t.length;
  if (!t.length) return s.length;
  const arr = [];
  for (let i = 0; i <= t.length; i++) {
    arr[i] = [i];
    for (let j = 1; j <= s.length; j++) {
      arr[i][j] =
        i === 0
          ? j
          : Math.min(
              arr[i - 1][j] + 1,
              arr[i][j - 1] + 1,
              arr[i - 1][j - 1] + (s[j - 1] === t[i - 1] ? 0 : 1)
            );
    }
  }
  return arr[t.length][s.length];
};

levenshteinDistance('duck', 'dark'); // 2