.▄▄▓▓█████████▓▓▄▄ ▄▓█████████████████████▓▄ ╓▓████████████████████████████▄ ▄█████████████████████████████████▓ ┌█████████████████████████████████████▄ ███████████████████████████████████████▌ ╫████████████████████████████████████████▄ ██████████████████████████████████████████ ██████████████████████████████████████████ ███▌ └▀▀████████████████████████▀╙ ▐██▌ ▐███ .▀▀████████████████▀▀ ███ ████ ╙▀████████▀▀└ ▄██▌ ████▓▓▄▄▄. .▄▄██████▄▄ ..▄▄▄▓████ ▀███████████████▀╒█▀████████████████▌ 4███████████████▀ ██ └███████████████▄ ╫███████▀▀╙▀████▌████▄██████▀▀╙╙▀██████████▌ └████████████████ (███╙ └ └ ▐██████████╩████▌ ███▐███▐██j████ ╫██¬███(██▐███¬ ▐██¬███(██▀███¬ ▐██═███(██▐███─ ▐██¬██▌(██j███ ▐██¬██▌(██ ███ ██¬██▌(██ ██▌ ╙╙- ╙ └
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⠀⢠⡆⠀⢠⣴⢶⣤⡀⠠⣶⣶⣶⣶⡆⠀⣶⠀⠀⢰⡄⠀⠶⢶⣶⠶⠀⠀⣶⣆⠀⣴⠀⠀⣠⣴⠶⣦⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⢶⣤⠀⠀⢠⣶⡄⠀⠀⣴⣶⠀⢰⡆⠀⠀⠀⠀⠀⠀⠀⢠⣴⠶⣦⠀⠰⣶⣶⣶⣶⡆⠀⣠⣴⣶⣄⠀⠀⣶⣦⣤⣄⠀⠀⠀⠀⠀⠀⠀⢸⡏⡇⢸⡇⠀⣿⠁⠀⠸⣧⠀⠀⢸⡇⠀⠀⠀⣿⠀⠀⣸⡇⠀⠀⢸⡇⠀⠀⠀⣿⢸⠀⣿⠀⢸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡏⠀⠀⠀⠀⠀⣼⠛⣧⠀⠀⣿⠘⡆⢸⡇⠀⠀⠀⠀⠀⠀⠀⢸⣇⡀⠀⠀⠀⠀⢸⡇⠀⠀⢰⡟⠀⠀⢹⡇⠀⣿⠀⠀⣻⡇⠀⠀⠀⠀⠀⠀⢸⡇⢱⢸⡇⠀⣿⠀⠀⢠⣿⠀⠀⢸⡇⠀⠀⠀⣿⠛⠛⢻⡇⠀⠀⢸⡇⠀⠀⠀⣿⠈⡇⣿⠀⢸⡇⠀⠶⣶⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⠀⠀⢰⣟⣀⣹⡆⠀⣿⠀⢳⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢷⡄⠀⠀⢸⡇⠀⠀⢸⣇⠀⠀⢸⡇⠀⣿⣶⠶⠟⠀⠀⠀⠀⠀⠀⠀⢸⠇⠘⣾⡇⠀⠹⢷⣤⡾⠃⠀⠀⠸⡇⠀⠀⠀⣿⠀⠀⢸⡇⠀⣤⣼⣧⣤⠀⠀⣿⠀⢳⣿⠀⠈⠻⣦⣤⣿⠀⠀⠀⠀⠀⠀⠀⠈⠿⣦⣤⡴⠀⣾⠉⠉⠉⣷⠀⢿⠀⠸⣾⡇⠀⠀⠀⠀⠀⠀⠀⢶⣤⣤⡾⠃⠀⠀⢸⡇⠀⠀⠀⠻⣦⣴⠿⠁⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡆⠀⠀⠀⣶⠀⣶⠀⠀⢰⡆⠀⠀⣴⣶⠀⠀⠰⠶⢶⡶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠶⢶⡶⠶⠀⠀⣴⠶⢶⡦⠀⠀⠀⠀⠀⠀⠀⢀⣴⠶⠶⡦⠀⢠⡶⠶⣦⡀⠀⣶⢆⢀⢶⡆⠀⠶⢶⡶⠶⠀⠀⣶⣶⠀⢰⡆⠀⣠⡶⠶⢶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⢀⢶⠀⣿⠀⣿⣀⣀⣸⡇⠀⢠⡟⢸⡇⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠘⢿⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⠀⠀⠀⠀⣿⠁⠀⠘⣷⠀⣿⢸⢸⢸⡇⠀⠀⢸⡇⠀⠀⠀⣿⠸⡄⢸⡇⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⢸⠀⡏⠀⣿⠉⠉⢹⡇⠀⣾⣅⣈⣿⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠉⠻⣦⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⠀⠀⣿⠀⠀⢠⡿⠀⣿⠀⠃⢸⡇⠀⠀⢸⡇⠀⠀⠀⣿⠀⣧⢸⡇⢸⣧⠀⠘⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠾⠀⠿⠇⠀⠿⠀⠀⠸⠇⠰⠟⠀⠀⠹⠇⠀⠀⠸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠾⠷⠶⠀⠰⠶⠶⠾⠟⠀⠀⠀⠀⠀⠀⠀⠈⠻⠶⡶⠶⠀⠙⠷⡶⠾⠃⠀⠿⠀⠀⠸⠇⠀⠶⠾⠷⠶⠀⠀⠿⠀⠸⠿⠇⠀⠛⠷⠶⠾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⢿⣻⣟⣿⣿⣿⣿⣿⢿⣿⣻⣿⡿⣿⣿⣿⡿⣎⢿⣻⣿⣿⣿⣿⣟⣯⣿⣿⣿⣿⢺⣻⣟⣿⢿⣟⣿⣻⣿⣿⣿⢿⢝⣯⣿⣿⣿⣿⣿⣿⢿⣽⣻⣿⣻⣿⣿⣿⣿⣟⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿
⣟⣿⣯⣿⢿⣾⣿⣽⣟⣯⣯⠳⣷⣻⢿⣿⣿⣿⣿⣧⠻⡽⣿⣞⣷⣳⣟⣯⣷⣿⣿⢸⣯⣿⣻⣯⢟⡾⣽⣷⣿⢯⢣⣿⢷⡿⣾⣿⡾⣟⣮⡿⣽⢷⣿⢿⣽⣿⣳⢿⣞⣷⣳⢿⣾⣿⣾⣿⣷⣿⣿⣾⣿⣿⡿⢟⢟⣿⣿⣯
⣟⡷⣿⣾⣿⣽⣾⣿⣻⣿⣻⣽⣆⡻⢯⡷⣿⣻⣽⣿⣷⡙⣵⣻⣽⣯⡷⣟⣿⣯⣗⢽⣺⣯⣿⡽⣯⣻⣯⣿⢓⡵⣟⣯⡿⣽⡿⡯⣫⢾⡷⣿⣽⣿⢿⣻⡿⣞⣿⣯⡿⣾⣻⣽⣿⣾⣿⣷⣿⣿⡻⣝⣝⣵⣾⢿⣿⣿⣿⡷
⣿⡽⣿⣾⡿⣿⣟⣿⡯⣟⣯⣷⢿⣺⣌⡛⢯⣯⢿⢿⣻⣿⣌⢾⣺⡷⣟⡽⣯⣿⢾⢸⣻⣗⣿⢽⣺⣽⡟⣪⣞⣿⣿⣻⣽⡿⣝⣾⣽⢿⣿⣻⢽⣺⡿⣯⡿⣟⣿⣞⣿⡿⣿⣿⣟⣿⢟⢏⣗⡵⣟⣯⣿⣽⣾⣿⣿⣿⣿⣟
⡷⣿⣟⣷⣿⣿⢿⣿⣿⣽⣞⣞⣟⣿⢾⣿⣦⡙⠿⡻⡙⢿⣽⣎⢾⡽⣟⣎⢿⢯⢿⡸⣿⡽⡺⡹⡽⡯⣺⣽⣿⣯⡿⣯⢗⣵⣻⣾⢿⣻⡯⣿⣻⣯⡿⡯⣟⣯⣷⣿⢿⢿⢟⢏⣇⣷⣯⣿⣳⣿⢿⣻⣽⣯⣷⡿⣯⢿⣫⡧
⡿⣯⣿⣟⣿⡿⣿⣻⣾⢯⡷⣷⣝⡺⣯⣷⣿⠫⡥⢪⢻⠄⣟⣿⣎⡻⢳⢵⢵⠽⡽⣞⣗⡷⠽⠿⢮⣯⣪⢛⢾⣯⡿⣽⣻⣾⡿⣽⣻⡷⣿⢿⣽⢯⣿⣽⢿⣻⢟⢏⣣⣵⡷⣿⣯⣷⣿⣾⣿⣻⣟⡯⣟⣾⣳⣿⣿⣿⣿⡯
⡿⣯⣷⣿⣿⣿⢿⣿⣽⢿⣽⢮⢿⣷⣦⠝⡱⡝⢀⣾⡗⢅⡛⣷⢟⣨⠟⢁⢠⠤⠦⢌⠉⢤⣖⡦⣄⠀⠻⡕⠲⢫⡾⣯⡿⣯⣟⣷⣻⣿⣻⣿⣯⣿⠿⠺⣙⣬⣶⣿⣯⣷⣿⡿⣯⡿⣗⣿⣞⣷⣯⣿⢿⡿⣿⢿⣿⣻⣿⡯
⡿⣯⣿⣟⣿⢿⢿⣽⣾⡿⣗⣿⢽⡺⣳⠽⠃⢌⣾⡗⠵⣿⣯⡏⡴⠁⡴⠊⢀⣤⣴⣤⣄⠀⠃⣈⡨⠀⠀⠟⢯⠸⣿⣻⢝⣷⢯⣿⣽⣾⡿⡳⡋⣦⣺⡿⣟⣿⣯⣷⡿⡯⣗⣯⢷⣻⡯⡷⣯⡪⣻⢾⣽⣻⣽⢿⣽⣯⣷⡯
⣿⣯⣷⣯⣭⣫⣛⣓⢗⢟⠷⠵⡯⢸⠁⠀⠌⠠⠈⠣⡱⣿⢝⢪⠃⣜⠍⡰⣽⡺⠾⠚⠚⠓⠈⣴⡴⣿⣽⢾⠌⢳⡕⢽⣿⣽⣿⡯⢟⢑⢥⢮⣯⢯⣿⣻⡿⣯⣟⡷⣯⣿⢷⣟⣿⢽⣯⢿⣾⣽⣽⢿⣞⣿⢾⡿⣟⣿⣟⡯
⣿⡾⣿⣻⡷⣯⣟⣿⣝⡯⣭⢽⠆⡇⠀⡌⣦⢆⡀⡐⡸⣋⣶⠟⢰⡳⢈⠮⠋⢀⠢⠬⠩⠉⠑⠌⡻⠉⡠⠠⢐⢘⢹⣖⢽⠞⡃⣕⣖⣽⣻⡿⣽⡻⣽⣽⣽⣷⣿⣻⣟⣾⢯⣿⡾⣿⣽⣿⢿⣾⣻⣟⣯⣿⣻⣽⡿⣯⣟⣏
⣿⣻⢟⣿⣻⢯⣿⣳⣿⣻⣟⣯⠂⣕⠀⠋⠟⠋⣰⡽⣸⣾⢃⠨⠨⡨⣮⣗⠢⠢⢐⢁⠂⢈⠓⠀⡰⠡⠀⠈⠲⡒⢠⡳⡕⡰⣼⣺⣽⣞⣗⣟⣾⢽⡷⣿⣽⣾⡷⣿⣾⣻⣿⢯⣿⣿⣯⣿⣯⢷⢿⣺⡫⣍⣗⢷⣿⣿⣿⡧
⣿⢷⣽⡽⣾⣻⣾⣟⣿⣟⣿⣟⢽⠃⢐⡐⡄⣺⢽⣊⣾⠧⠁⠌⢢⣫⣷⣟⣯⣎⢔⠠⠁⠅⣀⣧⢧⣆⠡⡩⡴⡴⡌⢣⡱⡿⣝⣷⣗⣿⣺⣽⣞⣯⣿⣿⣷⡿⣿⣿⣽⢿⢾⣻⣻⣽⣽⣾⣾⡿⡿⣼⣻⠝⣜⣷⡹⣯⣿⡗
⣿⡿⡷⣿⣻⣫⡿⡽⢝⣾⣷⢳⠃⠀⡜⢜⠄⠚⠹⣺⣿⠡⡅⠅⣕⣿⡣⢊⢚⢳⣁⢨⣠⣾⣻⣾⣻⡺⡢⣸⣯⠯⡋⣰⡇⡯⣿⣾⣻⣾⣻⣾⣻⡽⡿⣺⣫⢯⣯⣮⣾⣟⣿⣟⣿⣻⣯⣿⣾⢿⡣⡿⣽⡎⡪⣺⡧⣿⣿⡏
⡿⣛⣍⣥⣭⣮⣶⣿⣻⣿⡣⣟⢀⣆⠀⢏⠆⠀⠀⡘⢯⡇⠪⠐⢼⣯⡐⡀⠄⡍⡙⠓⡳⠻⠳⢛⠚⢋⠉⢅⣐⠴⢀⣾⢮⢿⣻⣞⡯⡟⢯⣫⣳⢽⣽⡷⣟⣿⢷⣿⣾⢿⣯⣟⣾⣳⣿⢷⣿⠟⣡⢯⢿⣇⠸⣸⣗⣿⣿⡏
⣷⢿⣽⣿⣽⣯⣷⣿⣝⢗⣽⠇⢐⣿⡀⠈⠂⢨⠀⠀⠣⡣⠁⢇⢮⡚⡪⡂⡐⡈⡈⡒⢒⢑⢑⢒⣑⣑⡉⡩⢐⠈⣰⡯⠫⢋⣍⣦⢮⣮⡷⡗⢟⠝⡳⠻⠻⡿⣻⣷⣿⢿⣯⣿⣟⣿⣽⡿⢑⣼⠝⣝⡋⢇⢇⣞⣞⢾⣿⡗
⣿⣻⡷⣿⣺⢯⡿⣞⢮⣯⠏⠀⠨⣿⢧⠀⠁⢐⡀⠀⠱⣌⠊⠀⠅⠍⡂⡑⠑⠕⢝⣞⡷⠽⠳⠝⠞⡊⡊⠐⣰⣞⣟⢆⣵⣛⣙⣙⡉⣊⣤⠶⠗⠛⠳⠿⢶⢦⢮⣬⣘⣙⣙⢛⢛⢝⣡⢶⣽⠁⡑⢄⠘⠨⠀⢳⡯⣫⣿⡯
⣯⣷⢿⣟⡾⡽⡝⣴⢽⠞⠀⠀⠈⣿⡿⢈⠠⡮⡂⠀⠀⣻⢷⡀⠐⣦⣤⣀⣁⡀⡀⠈⠈⠀⠈⡀⣀⢀⢀⣌⣕⣝⣊⣙⠓⢛⠋⡋⡉⠁⢠⡠⠂⢡⡖⠋⠂⠃⠑⠉⠟⠞⠯⠿⡽⣯⡿⠟⢫⢀⠠⢈⠄⠅⢢⢿⢝⣾⣟⡯
⣟⣾⢯⣿⢽⡫⣸⡾⢋⠄⠀⠀⠀⢿⣏⠀⠀⡏⠀⡀⠀⢎⢿⣆⠀⠠⠀⠙⠛⠛⠛⠛⠛⠚⠀⠈⠙⠙⠉⠋⠙⠛⠛⠿⠿⣿⣿⣿⢀⢰⡏⢀⢀⢏⢠⣰⣾⠞⢿⡿⠏⠉⠀⡁⠂⠀⡐⠌⠊⠄⠃⢁⣠⢦⢯⣷⢿⣯⣿⡯
⣻⢾⣻⣽⢯⢮⡟⣡⠃⠀⡁⠀⠀⠘⣷⠐⢠⠈⠀⣶⠀⠨⣳⢿⡇⠀⠀⠲⣶⣤⡘⠠⢧⣚⢾⣾⣄⠑⠲⣤⣨⣈⡛⢗⣖⡐⠍⢭⠀⣿⣇⠀⣿⣾⣿⣻⠃⢀⣾⠃⠀⠀⠂⠀⠂⠁⡀⣀⣂⣴⣞⣯⣿⣽⣿⢿⣿⣻⣽⡯
⣿⣟⣟⢎⣷⡟⡰⠁⠀⠄⢸⠀⡁⠀⠘⠇⠈⠂⣸⣿⣆⠀⡪⣟⣏⠀⢡⠀⠘⢿⣟⣷⣄⠑⢽⡽⣿⣷⣆⡉⠚⢞⢷⣆⡙⢿⣷⣔⠠⡨⣝⣧⠘⣿⣺⡏⠀⣴⣿⡄⠀⠄⠅⠊⠈⢎⡿⣵⢫⣳⣿⣿⣾⣿⣾⣿⢿⣽⣟⣯
⣿⣏⢮⢿⡞⡰⠁⠀⠨⠀⡦⡱⢷⣷⢔⠈⠂⠀⡛⡯⠃⡀⠘⢜⡇⠀⣜⢅⠀⠀⠻⣟⣿⣿⣤⡙⢳⣻⢿⣿⣶⣄⠀⠀⠀⠀⠛⡽⠀⠀⠀⢽⣇⠘⡙⠉⢠⣻⣿⠀⠠⠀⠂⠁⠀⢱⡟⡐⢱⢽⣿⣷⣿⣷⣿⣿⣻⣿⢾⣯
⣿⡪⣯⢟⢸⠀⢠⢂⠜⠨⠀⠄⡂⢹⣿⠕⠀⡀⠀⠀⢼⢧⠀⢑⢕⠀⢺⡅⠀⠀⠀⠙⣯⣿⣟⣿⣦⡈⠻⣽⢿⣟⣿⣦⣄⡀⠀⠀⠀⠀⠁⠀⠏⠕⠀⢀⣽⢝⣿⠀⠐⠀⠊⠎⢠⢸⠂⡌⣖⣯⣿⣿⣽⣿⣷⢿⣻⡾⣿⣯
⡷⣹⡝⡜⡔⠀⢐⠐⡁⠐⢈⠢⡀⣿⣻⠁⠐⠌⡢⠀⠈⠉⠀⠈⢪⠀⠸⣝⢄⠀⠠⠀⠈⢷⣿⣻⣟⣿⣶⣬⣻⡽⣟⣿⣿⣿⣶⠀⠀⠀⠂⠀⠁⠀⠀⡬⡚⢸⣿⠀⠐⠀⠡⡁⡎⡎⠢⣹⣽⣾⢿⣾⣻⡾⣟⣯⣗⣿⣻⣾
⣏⣾⠑⡇⡇⠀⠠⡐⡈⠐⢐⢑⠀⣿⣟⠀⢀⠁⠐⠈⠀⠀⠀⠀⠨⠀⠈⢚⡜⡄⠄⠀⠀⠈⢻⣽⣯⡿⣾⢿⡿⣿⣯⣷⢯⣻⣻⠿⠂⠀⠀⡀⠀⢄⢮⢪⣢⣿⣿⡀⠈⠀⢺⢸⢸⢐⠡⣳⡿⣽⣟⡾⡽⣯⢷⣻⣾⡽⣟⢾
⠮⣿⡀⢇⡇⠀⠀⡣⠐⢈⠰⡑⣐⣿⡗⠀⠀⠌⠀⠠⠁⠈⠀⠀⠀⠡⠈⠠⢸⡸⡰⡀⠄⠀⠀⠹⡽⣿⣽⣻⣟⣿⣯⣿⣿⣷⣅⠀⠀⠀⠀⡠⡸⡭⡫⢢⣿⣻⣾⢂⠀⢀⠕⠅⠌⣂⣧⡿⣿⣻⣗⣿⣳⡽⣽⣳⢷⡿⣵⡿
⣯⡚⣇⠸⣿⠀⠀⠘⡔⡀⢪⢪⣄⣿⡃⠀⠀⢂⠐⠀⠀⠐⠀⠀⡀⠘⠀⡅⡀⠹⣜⡆⡄⠀⠀⡀⠨⣈⠷⣷⣯⣷⡯⣿⣻⣿⣿⠇⠀⠀⡁⡮⡪⡳⣂⡾⠷⠛⠁⠈⠦⠍⢘⠠⣵⣳⣿⣻⣿⡽⣞⣾⣳⣟⣷⣻⡽⣯⢿⣿
⣿⣻⣔⡀⠻⡧⣧⠀⠘⠄⡐⡼⣽⣿⡂⠀⠀⠂⢀⠀⠁⢀⠁⠀⠀⠀⠈⣇⢂⠀⢿⣽⣎⠄⠀⠂⡀⠠⡓⣣⡻⣾⣻⣽⣯⣟⡟⠀⠀⠀⠐⢸⣸⡽⠛⠈⠀⠀⣀⣤⠖⣍⣥⡿⣯⣿⣯⡷⢯⢯⣗⡯⣷⣟⣷⣯⢿⣽⣻⣿
⣿⢿⣗⣗⢄⠈⢯⠳⢄⠑⠡⣫⡺⣿⣇⢀⠀⢈⠀⠀⠈⠀⢔⠀⠀⠀⠨⣷⡀⠅⠘⣗⣿⣷⢀⠀⠘⣔⠸⣻⣿⣮⣓⢷⣯⣟⣷⡄⠀⠀⠂⠂⠊⠀⠀⣠⡴⡟⠟⣨⣼⡿⣾⢿⣻⢷⣻⡽⣯⡻⡮⣻⣽⣟⣷⡿⣟⣯⣷⢿
⣿⣻⣟⣯⠊⣦⣀⠁⠠⠑⢅⢈⢞⢜⣿⡄⢀⠀⠀⠀⠂⢅⠅⠕⢐⣰⠀⢿⣇⠨⡀⠘⣞⣿⣷⣷⡀⠈⠧⡱⣻⢾⡿⣷⣮⣻⣎⠅⠀⠀⠀⠀⠀⢀⡾⣽⣺⣞⣿⣯⣷⣿⣟⣯⡯⣿⢽⣯⢷⣫⢯⢿⣾⣻⣯⣿⣿⣻⡾⣿
⣿⣽⣯⣿⢷⢬⡹⢦⠀⠁⡊⢮⣇⠂⢽⣿⡆⢀⠀⢂⠕⢁⠊⣠⣿⠿⠀⢸⣿⣣⡈⠢⠘⣞⣿⣿⢿⡢⣠⠈⠌⠯⣿⣻⣿⢷⡿⡂⠀⠀⡀⠄⢠⡯⣻⣽⣯⢿⣽⣾⣟⡷⣯⣷⢿⢯⣻⣾⣻⣽⣻⣯⣿⣯⣿⢿⣾⢽⣻⣻
⣿⣾⢿⣾⣿⢟⠟⣘⣷⡀⠈⢢⠇⢱⡼⣿⣻⣆⠰⡨⠐⠀⣰⠏⠁⡔⠁⠀⢻⣾⣻⡄⢁⢘⢞⣿⡜⢻⣿⣷⡀⠉⢎⢿⣺⠏⠂⠀⢠⣷⠀⠠⡿⡕⣿⣳⡿⣟⣿⢳⢯⣿⣻⢾⣟⣯⡿⣞⣷⣻⢾⢾⣷⣿⣻⣿⡽⣿⢽⣽
⣿⣿⠟⡣⡯⠺⠚⠟⠛⣃⢀⡞⠁⢺⣿⣻⣽⢟⠐⠈⣠⠞⠁⡀⠂⠁⠠⠀⡂⢿⣽⢿⡄⡀⢑⢿⣿⡄⠉⠻⣿⡶⣄⠉⠪⠁⠀⠀⢸⡗⠀⡀⠹⡕⣟⣷⢿⣟⣗⣿⣻⣺⡽⣯⣿⢷⣻⣯⣯⡿⣯⢿⣷⢿⣯⣷⢿⢽⣽⣻
⣿⢇⡯⡟⠀⠌⢢⢨⠐⢀⠉⠀⢀⣽⣿⡟⢁⠀⣰⣿⡏⠀⡴⡨⠀⠀⢐⠀⠰⠘⣿⣯⡻⡄⠠⠑⣯⡿⣆⠀⢈⠉⢛⢴⡄⠀⠀⠁⠄⠁⣸⡇⠀⣇⢯⡿⣟⣯⣯⣷⣻⡺⣽⢿⣾⡿⣮⣷⣿⣽⢿⣽⢾⣿⣽⣿⣻⢽⡾⣽
⣿⢕⡿⢀⢬⢐⡡⡅⡣⠐⠈⠀⣸⡿⠯⠛⡡⢊⣿⣿⡂⢐⡕⡅⡁⠄⣸⡆⠈⢧⠘⣿⣟⡧⡅⠐⠘⣽⣻⣧⡀⠌⡠⣿⡏⡀⠀⢠⠄⢠⡇⣁⠀⢪⢪⡿⣿⣿⢿⣾⣳⢿⣽⣿⣯⣟⣷⣻⣞⣿⣻⡽⣟⣯⣷⣿⣟⡮⣟⣿
⣿⣇⢯⠐⣕⢔⣽⡽⠊⢀⣀⣈⣤⣴⣾⠏⣰⣾⣿⣿⠀⢸⣸⢪⠀⠀⡾⣗⠄⠁⢷⡈⣿⣿⣻⢔⢁⠈⢾⣝⢿⣦⣥⣿⡇⠄⠀⡘⠀⣾⢝⢾⡆⢘⡮⣟⣿⣾⣿⣿⢽⣿⣻⣾⢿⡽⣾⣿⣽⣿⣽⣟⣿⣟⣿⣽⣷⡯⣿⣿
⣿⣿⡎⢆⠹⡗⣟⣷⣟⣯⢿⢽⣻⠟⢀⣼⢷⣿⠿⠋⠀⢸⣺⣝⠄⠁⠝⣿⣵⠀⠉⢷⡌⣟⣿⣿⣲⠠⠂⠽⡽⢽⣷⣿⡝⠠⠀⠀⣸⡯⣇⢯⡇⠀⣯⢿⣽⣿⣽⣾⣽⣾⢿⣽⡿⣽⢿⣾⣻⢾⡷⣟⣷⣟⣯⡷⣿⢽⣻⣾
⣿⣿⣽⣆⢳⣄⡉⠙⠙⠚⠓⢙⠀⠔⢟⠻⠿⣷⣦⡐⣄⡵⡕⡕⡁⢐⢜⣽⣾⣷⡀⠈⠻⢿⣷⣻⣷⡭⡘⠄⡉⠪⡚⢯⡆⡁⠀⠀⣾⢯⣗⢽⡂⠀⣻⡽⣷⢿⣻⣷⣿⣻⣿⣽⣿⡽⣯⣿⣽⣻⣟⣿⢷⡷⣷⢿⡽⣯⢷⣿
⣿⣿⢷⡿⣧⣎⣍⣋⡫⢫⢯⣯⣗⡖⠀⢀⠀⠙⡻⡸⣞⣯⢧⡣⠀⠐⠹⣽⣾⣿⣽⣄⠀⠉⢿⣻⢿⣻⣶⡄⠂⢁⢧⡊⣿⠅⠀⢈⢺⣻⢮⢏⡏⠀⢸⣯⣿⣻⣟⣿⣽⣿⣽⣾⣷⣿⣟⣷⡿⣞⣷⣟⣿⣻⣟⣿⣻⣟⡿⣾
⣿⣟⣿⣻⣯⡿⣯⡿⣟⡷⡮⣎⢷⡇⠀⢔⠐⡀⢰⢼⡯⡯⣗⠏⠀⠀⡀⠸⣿⣾⣷⡿⡵⠀⠀⠉⠻⢽⢕⠻⢧⡀⠢⣟⣿⡕⠀⠠⠱⣯⣻⣺⢢⡆⢸⣿⢾⡷⣿⣽⢿⣽⣯⣷⡿⣾⡿⣽⢿⣻⣷⣻⡽⣮⢯⣯⣟⣾⣻⣽
⠝⡑⡁⡃⡫⢿⣻⣽⡏⣏⢟⣞⠮⣳⠀⢙⠨⢀⣼⣫⡫⣐⢕⠁⠀⠀⠀⠘⣿⣺⣳⢟⠁⠀⠄⠀⠀⠀⠑⠁⠀⡀⠀⠈⠛⠇⠀⠨⢘⢷⢕⢗⢽⠁⠸⡿⣯⢿⣻⣞⣯⡷⣟⣷⣿⣻⣽⢯⢿⢽⢾⣷⠟⠉⣈⣀⣀⢁⠉⢻
⡰⡰⢫⣳⠬⡐⠙⠪⠻⣜⢜⢜⣎⡞⣕⡀⠈⠓⠷⠓⠙⠂⠏⡆⠀⣳⡀⠁⠀⠄⠂⠀⠀⡐⠀⠠⠈⣸⠇⣰⣦⣦⣄⣀⠁⠀⠀⢁⠀⠁⠁⠁⠇⡌⢐⡯⣟⣧⣻⣽⣿⣽⣟⣿⡾⣿⡽⣽⣺⣯⣯⠇⢠⣞⣮⣖⣬⣄⡁⣸
⣿⣟⢔⡢⡑⢕⠀⠑⢁⠪⢮⢳⡳⣽⣮⣏⣖⢤⢤⢦⢮⣲⡤⠄⠀⡺⢵⢦⡤⡤⡆⠂⣰⠤⡖⡅⢰⡷⠠⣻⡿⣿⣿⣻⡆⠀⠀⠘⢽⣟⣷⢦⣄⣀⢽⡏⣿⣽⣿⣻⣷⢿⣽⡷⣟⠗⡙⠑⠫⠳⠇⢠⢿⣟⣗⣝⣝⠟⣿⢿
⡿⡗⡿⣣⢣⢃⠈⢀⠀⠀⡈⢜⢺⣷⣻⡷⣿⣯⣷⡿⣕⡝⠄⢀⢮⡿⡞⡌⣎⡗⠂⢸⣷⣵⠀⠃⣿⢏⢸⣜⣿⣿⢯⡳⡇⠀⠅⡂⠀⣿⣺⢛⣃⢓⢉⣂⣽⣿⣾⡿⣿⣿⡻⠝⠁⣠⡲⡓⣑⡐⡄⡬⠧⡳⣷⣵⡽⣅⢾⣿
⣿⡿⡊⢪⢪⢐⢬⣲⡇⠕⠀⠐⠐⠨⡚⡽⣿⢾⣻⢕⡽⠠⠀⣞⣿⣗⢧⠳⡉⠆⢠⣿⡿⠟⣈⡴⡟⡬⣟⢜⣿⣿⣽⡻⣵⠀⠘⢌⣄⠈⢿⢐⣽⣽⡿⣼⡿⣾⣿⢿⣻⣾⡻⠈⢸⠕⣜⢴⡳⢗⢽⣜⠕⠁⠑⠑⠙⢇⣾⣿
⣿⠓⠘⣾⢍⣮⢺⣾⡝⣎⠄⢂⢕⢄⢊⢺⣽⡿⣿⢸⢇⠬⢀⡿⡾⠧⢒⡡⠅⠀⠼⠋⢀⣞⣯⡾⡨⡯⡗⣽⣿⣿⣷⣿⣵⡀⠠⠀⢳⡀⢝⠐⡿⣞⣿⣟⣿⣿⠝⠋⠉⠈⠁⠀⢈⡡⣌⣙⠨⣾⣟⠠⣴⣿⣽⣻⣶⠨⣾⣻
⣧⡏⠢⣨⠌⠸⣽⡾⡵⡬⡱⡸⡨⠀⠂⠙⠯⣿⣻⡵⡑⠌⡞⢠⡴⠒⠁⠀⡄⡄⡦⡦⣾⣿⢯⢇⢝⢾⡃⣿⣿⡿⣟⣿⣿⣿⣾⡆⠸⡀⡼⠀⣻⣷⢿⣽⡿⠁⢢⣪⢿⣳⡷⡶⡙⣿⡷⣥⣷⣕⣗⢀⢋⣙⢚⠝⢞⢕⣽⣿
⣿⡱⠱⢘⠡⢡⢦⠈⣳⣽⡷⡽⡝⡀⡧⡣⣢⡈⢳⢿⣎⡂⠐⢛⠠⢙⣕⣕⣙⣚⠯⣟⣿⢽⣇⡽⣼⣹⣺⡿⢿⣿⣿⡿⡿⢿⡚⢃⢀⡤⠇⣁⣿⣾⣿⢯⡧⠈⣾⠺⣟⡟⢨⢣⣲⢾⣗⣿⣻⡏⣮⣶⣔⡴⣝⡆⡈⣿⣿⣽
⣇⠃⡔⠡⡈⡂⡹⣸⢼⢽⣿⣿⣳⢢⡇⢗⢵⡑⢄⡣⡓⡇⠕⡟⠯⠳⡉⠫⣯⣿⡶⣵⠉⡙⢙⠙⠉⢱⣐⡚⡒⡂⡒⣓⣝⣝⡼⢖⠏⢊⣰⡾⣟⡷⠟⠛⠃⠀⠈⡁⣁⡄⡁⢿⢺⣻⡿⡻⢋⣮⣾⣾⡿⢋⠙⣯⣗⢕⣿⣿
⡇⡜⣼⡇⢶⢘⣮⢮⢯⢯⣯⡫⡞⣵⣟⠢⡓⡔⠵⣹⣺⣬⢱⣲⢽⣳⢯⡃⣽⠯⡿⢟⢐⠐⡕⠡⠁⢺⡽⣹⣬⣬⣬⣪⡬⣴⡴⣶⡲⣯⣷⡿⠋⠠⢰⢴⡕⠠⣾⣽⠿⣷⣦⢏⢪⠏⣥⣾⡇⣿⣻⣿⡁⠢⣞⡿⣯⢳⣻⣿
⣷⣕⣯⣿⢵⣟⣮⣫⡯⣿⣿⣯⣯⣯⣳⡯⣧⣧⢣⡪⣺⡿⣧⣻⣯⣯⣿⡢⡿⣶⡖⡑⣀⡘⢕⠌⡘⡄⢻⣺⣽⣷⣿⣯⣿⣯⣟⣷⣯⣷⣷⡯⠀⡯⣾⣟⣧⡈⢿⠡⣼⣿⣯⣿⢸⡅⣿⣿⣿⣮⣏⣧⣵⣽⣷⣿⢯⣯⣿⣿
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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠤⠒⠒⠒⠒⠒⠒⠒⠒⠢⠤⢀⠀⠀⠀⠀⠀⠀⠀⠤⠄⠀⠠⠤⠤⠤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠤⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠀⠀⠀⠀⠀⠀⠀⣀⠀⠤⠤⠤⠐⠀⠀⠤⠤⠤⠵⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⣀⠔⠉⣀⠠⠤⠀⠐⠒⠒⠒⠂⠀⠠⠤⠤⢀⠉⠒⠤⠤⠔⠒⠂⠀⠉⠉⠉⠁⠒⠒⠨⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠈⢀⠄⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠄⠀⠒⠀⠈⠉⠉⠉⠉⠉⠁⠒⠀⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢑⡄⠑⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠄⠒⠒⠒⠒⠒⠒⠂⠒⠂⠀⠈⠒⠂⠐⠊⠐⠒⠊⠆⠈⢂⠀⠀⠀⠀⠀⠀⡀⠤⠔⠒⠒⠒⠊⠂⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⢀⡤⠤⠒⠒⠈⠀⠀⠈⠁⠉⡉⠉⠐⠒⠤⣀⠈⠉⠀⡒⢄⠀⠸⡀⠀⠀⠀⢀⡪⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⢀⠔⠁⡠⢄⣒⣊⣉⣉⠁⠀⠤⠄⣈⠉⠍⠂⠄⠈⠁⠓⠄⠀⠢⢕⢄⠈⢠⢀⠔⠁⡠⠔⠊⢉⣀⣀⣀⣀⣀⡈⠁⠒⡀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⣀⢀⡀⠈⠉⢠⣤⣤⣤⡤⠀⢀⡀⠀⠀⠀⠀⠀⠀⣶⣶⣶⣦⣌⠀⠀⠘⠄⠰⠀⡰⠃⠀⠀⠀⠀⠀⠀⠀⢠⣉⠙⠱⢄⠁⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢒⠤⢄⣉⠛⠀⠀⠈⣅⠀⠀⣶⣿⠆⠀⢸⣿⣿⣿⣿⣧⠈⢦⠀⢈⠈⣠⡆⠀⠘⠃⠀⠀⣴⡄⠀⣿⣿⣶⣦⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⡀⠑⠱⡠⢀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⠿⠇⠈⠠⡆⠰⠿⠅⠀⠈⠃⠀⠀⠉⠁⢀⣿⠿⠛⣁⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢄⡈⠀⠒⠛⠁⠒⠤⠤⠤⠌⢉⣉⠉⢁⣤⠶⠒⠂⠀⠃⡒⠲⠤⠤⠤⠄⠤⣤⠤⠤⠤⠤⠴⠚⠁⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠤⢄⠀⠀⠀⠀⠀⠀⠈⠁⠒⠒⠒⠒⠤⠄⠤⠤⠤⠤⠤⠄⠀⡠⠔⠊⠀⠀⠀⠒⠤⡀⠀⢀⣀⡀⢀⠔⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⣀⣤⡤⠈⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠠⠒⠁⠠⠊⠈⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄⠁⢆⠀⠐⠒⠒⠈⠀⠈⡄⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠁⠀⠀⠤⠤⢄⣀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠒⠊⠁⣀⡠⠤⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠀⠃⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⠁⠀⠀⠀⠀⠀⠀⠈⠁⠒⠒⠠⠤⠤⢔⣒⣒⡈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢀⣀⣀⠀⠁⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠐⠒⠒⠒⠂⠀⠤⠤⠤⠤⠤⠀⠀⠀⣀⣀⣀⣀⠀⠀⠤⠤⠄⠂⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢀⠊⠀⠀⠀⢡⠀⠈⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠈⠀⠀⠀⠀⠀⡆⠀⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠢⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠐⠤⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠒⠒⠂⠠⠤⠤⠄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⢀⣀⣀⣀⣀⠤⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠘⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠁⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠐⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠠⠒⠑⠀⠀⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠄⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⢄⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⠈⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄⠀⠀⠀⠀⣀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠄⢀⣀⣀⠤⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠤⢀
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