⠰⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡄⠠⣔⠝⠁⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⡀⠀⠀⠀⠀⠀⠀⠀⢐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡵⠊⠀⠀⠸⠄⠀⠀⠈⠒⠐⠂⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢀⠄⠊⢀⠀⣟⣠⣤⣦⣶⣤⡄⠈⣄⠏⠀⠀⠀⠀⠀⠀⢀⠠⣤⡵⠞⠁⠀⠀⠀⠀⣹⢃⠀⠀⠀⠁⠆⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢠⠆⠁⠀⠀⡾⠀⣿⣿⣿⢏⠙⠏⢐⣱⣿⣮⠟⣦⣀⢀⠠⢆⣵⠾⠊⠀⢀⠀⠀⠀⠀⠀⣏⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢠⠃⠀⠀⠀⢠⠃⢠⣿⢿⢋⠢⠠⠎⠀⠼⡿⠃⠫⠾⢯⢥⣾⠞⠋⠀⠀⠀⠈⠫⣖⢤⣀⣈⢾⡹⢇⡀⣤⠤⠖⠀⠀⠀⠀⠀⠀
⠀⠀⢀⡇⠀⠀⠀⢀⡾⢤⣾⡟⢕⣐⣠⣤⣤⣤⣄⠇⠚⣥⡶⣭⣿⣿⣄⠀⠀⠀⠀⠀⠀⠈⠪⡳⣝⢮⡝⣧⢻⡼⠁⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣾⣷⠀⠀⡴⣺⣥⡞⠵⠾⣟⣿⣿⣿⣿⡿⣿⢷⡾⡵⢻⡻⣟⣿⣿⣧⠀⡐⣀⠀⠀⠀⢀⢼⡹⢮⡝⣮⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢰⣿⣿⣆⠀⠨⣋⠀⡔⠡⢂⠌⠚⠿⣿⣯⣟⣮⢳⣭⣛⢦⡙⢽⣺⣽⢿⣷⣄⠤⠀⠀⣠⢎⣷⠹⢧⡻⡜⣧⢳⡄⠀⠀⠀⠀⠀⠀⠀
⠀⢸⣿⢿⣿⠀⢓⣬⣿⣶⣷⣤⣒⠈⡘⡝⢿⣟⣮⢳⣎⡽⣺⣷⣅⠻⣼⢯⣿⣿⣇⠀⠔⠉⠈⠀⠈⣷⣽⣦⣤⣬⣼⣂⡐⠀⠀⠀⠀⠀
⠀⢾⣿⣿⣿⡀⣤⠈⠉⣿⣴⡾⣿⣿⣶⡰⠀⠛⢯⣷⢾⣱⢗⡾⣹⢷⣣⢟⡻⣾⣿⡿⣶⣶⣶⣶⣿⢿⣻⡽⣟⣿⣻⣿⣿⣶⣄⠀⠀⠀
⠀⢋⣿⣿⣿⣇⠸⡂⢀⠈⢛⠓⠶⢎⡁⡏⠀⠀⠈⢻⣿⣽⣻⣼⡳⣏⣿⣯⣳⢧⣿⡝⣧⠻⡜⡧⢯⣛⢧⠿⣽⣞⡷⣯⣟⣿⣿⣧⡀⠀
⠀⢸⡲⣙⢾⣿⡀⢻⡀⡒⠄⡑⠃⠄⠀⠀⠀⠀⢠⡀⠉⠛⣿⡾⣽⣳⣟⣿⢿⡷⣾⡻⣌⢳⠹⣜⣣⠝⣎⡛⡶⣹⢻⡽⣞⣯⢿⡿⣷⡄
⠀⠀⣟⠶⣥⡛⣇⠀⠹⣳⠷⣤⣁⠂⠄⠀⠀⢀⡀⣀⣠⣼⣟⣿⣷⣻⢾⣽⡳⢮⡙⣷⡍⢖⡹⢦⡏⣞⠦⣝⡳⣭⢷⡻⣽⢎⣯⣟⣷⣿
⠀⠀⠘⡝⡶⢻⣽⡀⠀⠘⢌⠳⣫⢟⣮⣔⢼⢻⠻⣿⣽⢿⣻⢷⣫⣟⣧⣏⢿⢣⣝⡼⣞⣥⣛⢶⠻⣬⠳⡵⢻⡜⢧⣟⣧⣟⡷⣿⢾⣽
⠀⠀⠀⠘⣕⠫⡜⣇⠀⠀⠀⠢⠀⠙⠢⣟⢿⡄⠓⢹⢾⡿⣽⣫⡗⣯⠾⢭⡛⢷⢮⣷⣹⣶⢩⢎⡳⢥⡛⣜⡣⢞⣣⢞⠶⣩⠟⣯⢿⣾
⠀⠀⠀⠀⠈⠳⡆⢼⡄⠀⠀⠀⠀⠠⠀⠈⠫⢿⣷⢻⡞⣴⢧⠶⣭⢦⡟⣶⣛⣞⡻⡼⢛⠿⠿⢏⡿⢯⣟⣯⣟⣧⣽⣊⣏⢗⡻⣬⠳⣞
⠀⠀⠀⠀⠀⠀⠙⠦⣳⠈⠄⢀⠀⠀⠄⠁⢀⠈⠻⣧⠜⡡⢎⠓⡌⠂⠔⣂⠒⡌⣒⠭⣘⠬⢙⠢⡘⠢⠜⣈⠛⠾⣳⣟⡾⣬⢳⠼⣹⢜
⠀⠀⠀⠀⠀⠀⠀⠀⠺⣧⣔⠀⠂⠄⠠⢀⠀⠠⡰⠹⠪⡣⡌⠊⠄⠁⠐⠀⠘⢠⠁⡒⠩⠎⣄⠓⠨⠁⠌⠠⠉⠤⡈⠜⢿⡹⣷⣙⢦⢫
⠀⠀⠀⠀⠀⠀⠀⠀⡌⠌⠟⢿⠶⣬⣐⡀⣌⠰⠁⠂⣧⢑⡵⣌⠀⠀⠂⡀⠈⠀⠐⠈⠱⡈⢆⠉⠄⠁⠀⠁⣈⠐⠤⡈⢌⡳⡝⣞⢮⠱
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣤⣈⢆⠈⢐⠈⢍⣋⠅⡌⠱⣾⣿⣧⢳⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐⠀⠂⠀⢀⠰⢠⠘⡘⢤⠓⡼⣰⠹⡜⣪⢧
⠀⠀⠀⠀⠀⠀⠀⢀⡧⠀⠉⠓⠷⢥⣑⢔⠐⢏⠀⠉⢹⣿⠓⢼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⢌⡑⠬⡙⡴⣃⢯⣱⠡⢎
⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⠀⠀⠀⠀⠀⠉⠛⠶⣝⡲⡈⠈⡇⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠡⢂⡜⡰⣉⠖⣩⠖⡥⣏⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣄⠂⡸⡘⣄⠀⠀⢀⠀⠄⡀⠂⠄⡐⢄⠂⡐⠠⠃⢆⠬⡑⡌⣎⡱⢎⡵⣚⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠑⠁⠉⠪⡣⡰⠀⣅⠢⢡⠘⢠⡑⠢⢌⠠⢃⡼⠆⠚⠉⠘⠢⢗⡮⣔⡩⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠵⢦⣉⡦⣉⠖⣨⡣⠼⠚⠁⠀⠀⠀⠀⠀⠀⠀⠉⠢⣝⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⡀⠀⠀⠀⠀⠀⠀⠀⢐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡵⠊⠀⠀⠸⠄⠀⠀⠈⠒⠐⠂⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢀⠄⠊⢀⠀⣟⣠⣤⣦⣶⣤⡄⠈⣄⠏⠀⠀⠀⠀⠀⠀⢀⠠⣤⡵⠞⠁⠀⠀⠀⠀⣹⢃⠀⠀⠀⠁⠆⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢠⠆⠁⠀⠀⡾⠀⣿⣿⣿⢏⠙⠏⢐⣱⣿⣮⠟⣦⣀⢀⠠⢆⣵⠾⠊⠀⢀⠀⠀⠀⠀⠀⣏⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢠⠃⠀⠀⠀⢠⠃⢠⣿⢿⢋⠢⠠⠎⠀⠼⡿⠃⠫⠾⢯⢥⣾⠞⠋⠀⠀⠀⠈⠫⣖⢤⣀⣈⢾⡹⢇⡀⣤⠤⠖⠀⠀⠀⠀⠀⠀
⠀⠀⢀⡇⠀⠀⠀⢀⡾⢤⣾⡟⢕⣐⣠⣤⣤⣤⣄⠇⠚⣥⡶⣭⣿⣿⣄⠀⠀⠀⠀⠀⠀⠈⠪⡳⣝⢮⡝⣧⢻⡼⠁⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣾⣷⠀⠀⡴⣺⣥⡞⠵⠾⣟⣿⣿⣿⣿⡿⣿⢷⡾⡵⢻⡻⣟⣿⣿⣧⠀⡐⣀⠀⠀⠀⢀⢼⡹⢮⡝⣮⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢰⣿⣿⣆⠀⠨⣋⠀⡔⠡⢂⠌⠚⠿⣿⣯⣟⣮⢳⣭⣛⢦⡙⢽⣺⣽⢿⣷⣄⠤⠀⠀⣠⢎⣷⠹⢧⡻⡜⣧⢳⡄⠀⠀⠀⠀⠀⠀⠀
⠀⢸⣿⢿⣿⠀⢓⣬⣿⣶⣷⣤⣒⠈⡘⡝⢿⣟⣮⢳⣎⡽⣺⣷⣅⠻⣼⢯⣿⣿⣇⠀⠔⠉⠈⠀⠈⣷⣽⣦⣤⣬⣼⣂⡐⠀⠀⠀⠀⠀
⠀⢾⣿⣿⣿⡀⣤⠈⠉⣿⣴⡾⣿⣿⣶⡰⠀⠛⢯⣷⢾⣱⢗⡾⣹⢷⣣⢟⡻⣾⣿⡿⣶⣶⣶⣶⣿⢿⣻⡽⣟⣿⣻⣿⣿⣶⣄⠀⠀⠀
⠀⢋⣿⣿⣿⣇⠸⡂⢀⠈⢛⠓⠶⢎⡁⡏⠀⠀⠈⢻⣿⣽⣻⣼⡳⣏⣿⣯⣳⢧⣿⡝⣧⠻⡜⡧⢯⣛⢧⠿⣽⣞⡷⣯⣟⣿⣿⣧⡀⠀
⠀⢸⡲⣙⢾⣿⡀⢻⡀⡒⠄⡑⠃⠄⠀⠀⠀⠀⢠⡀⠉⠛⣿⡾⣽⣳⣟⣿⢿⡷⣾⡻⣌⢳⠹⣜⣣⠝⣎⡛⡶⣹⢻⡽⣞⣯⢿⡿⣷⡄
⠀⠀⣟⠶⣥⡛⣇⠀⠹⣳⠷⣤⣁⠂⠄⠀⠀⢀⡀⣀⣠⣼⣟⣿⣷⣻⢾⣽⡳⢮⡙⣷⡍⢖⡹⢦⡏⣞⠦⣝⡳⣭⢷⡻⣽⢎⣯⣟⣷⣿
⠀⠀⠘⡝⡶⢻⣽⡀⠀⠘⢌⠳⣫⢟⣮⣔⢼⢻⠻⣿⣽⢿⣻⢷⣫⣟⣧⣏⢿⢣⣝⡼⣞⣥⣛⢶⠻⣬⠳⡵⢻⡜⢧⣟⣧⣟⡷⣿⢾⣽
⠀⠀⠀⠘⣕⠫⡜⣇⠀⠀⠀⠢⠀⠙⠢⣟⢿⡄⠓⢹⢾⡿⣽⣫⡗⣯⠾⢭⡛⢷⢮⣷⣹⣶⢩⢎⡳⢥⡛⣜⡣⢞⣣⢞⠶⣩⠟⣯⢿⣾
⠀⠀⠀⠀⠈⠳⡆⢼⡄⠀⠀⠀⠀⠠⠀⠈⠫⢿⣷⢻⡞⣴⢧⠶⣭⢦⡟⣶⣛⣞⡻⡼⢛⠿⠿⢏⡿⢯⣟⣯⣟⣧⣽⣊⣏⢗⡻⣬⠳⣞
⠀⠀⠀⠀⠀⠀⠙⠦⣳⠈⠄⢀⠀⠀⠄⠁⢀⠈⠻⣧⠜⡡⢎⠓⡌⠂⠔⣂⠒⡌⣒⠭⣘⠬⢙⠢⡘⠢⠜⣈⠛⠾⣳⣟⡾⣬⢳⠼⣹⢜
⠀⠀⠀⠀⠀⠀⠀⠀⠺⣧⣔⠀⠂⠄⠠⢀⠀⠠⡰⠹⠪⡣⡌⠊⠄⠁⠐⠀⠘⢠⠁⡒⠩⠎⣄⠓⠨⠁⠌⠠⠉⠤⡈⠜⢿⡹⣷⣙⢦⢫
⠀⠀⠀⠀⠀⠀⠀⠀⡌⠌⠟⢿⠶⣬⣐⡀⣌⠰⠁⠂⣧⢑⡵⣌⠀⠀⠂⡀⠈⠀⠐⠈⠱⡈⢆⠉⠄⠁⠀⠁⣈⠐⠤⡈⢌⡳⡝⣞⢮⠱
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣤⣈⢆⠈⢐⠈⢍⣋⠅⡌⠱⣾⣿⣧⢳⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐⠀⠂⠀⢀⠰⢠⠘⡘⢤⠓⡼⣰⠹⡜⣪⢧
⠀⠀⠀⠀⠀⠀⠀⢀⡧⠀⠉⠓⠷⢥⣑⢔⠐⢏⠀⠉⢹⣿⠓⢼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⢌⡑⠬⡙⡴⣃⢯⣱⠡⢎
⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⠀⠀⠀⠀⠀⠉⠛⠶⣝⡲⡈⠈⡇⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠡⢂⡜⡰⣉⠖⣩⠖⡥⣏⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣄⠂⡸⡘⣄⠀⠀⢀⠀⠄⡀⠂⠄⡐⢄⠂⡐⠠⠃⢆⠬⡑⡌⣎⡱⢎⡵⣚⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠑⠁⠉⠪⡣⡰⠀⣅⠢⢡⠘⢠⡑⠢⢌⠠⢃⡼⠆⠚⠉⠘⠢⢗⡮⣔⡩⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠵⢦⣉⡦⣉⠖⣨⡣⠼⠚⠁⠀⠀⠀⠀⠀⠀⠀⠉⠢⣝⣆
