Explanation:
https://tio.run/##jVQ9bxNBEO39K0Zp7iycKHFSWUKIFkGIMF0u6NZ3a9@S9a7ZjyQWhAIkC0VyBEKRaGigoUCiSkPJT7k/Ymb2nMs5uGCL097OzJt5M2@XTeRmPmVSjxaLfjn7@LoFUM5/466c/8TdV2AnWuRwwqTnwI3RBsQQMiYlz@FUuEJ7t7QyY9i0hQAT5hw3yi5RVhdhCiWcYFJYXvs2wjoUd/EuSpP8Xho1wg63j2DAsmMnsmPMLlTOzyAWymlwBa@rGPkxV669DvHwRXp0gxkQd1YQ@dnEcGuFVhCP2RSUdpBp5ZhQtZtdB5wkdaFL4G4FbCWzRR27NtJv4XqTJFtRFbnbjJSc3IGpnNq@4TeIqYKh9gYKZJ@LkXCWmt73A@toggHF0p9w3hGXoVdZ2GzeDA73nGUFjJnLihYV3b1fzq@3Dqrq9v24FzUY3Zne8IYFKD8eYHnItgdecZuxCW@yBdi9i1teXj3qP92PNqIOWZ5QBR38@wcbG9GDCarrldeOWxys9tiG0AqFHjgqB8wCoUGVugX/uygXl6g/0lRcKSkICcXfBhQ5KSN@eP…