⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⠐⠦⡀⠀⠀
⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⡈⠥⣀⠀⠀⠀⠀⠀⠀⠄⢠⠀⠀⠈⢆⠀⢹⡄⠀
⠀⡔⣄⡘⠄⡃⠀⠀⠀⢠⢶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠐⠢⠀⠀⠀⠀⠀⠀⠀⠱⡀⠘⣄⠀⠀⠀⠀⢶⠀
⠸⢐⡯⠄⠰⠁⠀⠀⢠⢏⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣃⠴⡉⡄⠘⡆⠀⠀⠥⣘⠆
⠐⠈⡶⢀⠘⡀⠀⠀⢾⡄⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠐⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢫⠴⡙⡄⢧⠀⠀⢰⠈⡧
⠂⠐⡳⠀⠸⡀⠀⠠⢳⡜⠁⠀⠀⢀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠃⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡣⡍⠇⣸⠀⠀⡘⠄⣣
⠰⠀⠹⡁⠄⣃⠀⢨⡓⣎⠀⠀⢀⠎⢐⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡖⢈⣅⣀⣀⣀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡕⣹⢂⢘⠀⡜⢁⢢⠃
⠀⢣⡌⢳⢀⢸⡀⢠⢻⡔⡀⠀⠀⡇⢸⡄⠀⠀⠀⠀⠀⡀⣀⠔⡰⢢⡐⢦⣸⡑⢦⢎⡵⢊⡄⠳⡀⢱⢤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⡰⡽⢁⠊⣼⢊⡐⠌⡜⠀
⠀⠀⠹⡄⢇⠂⣗⡫⢇⡾⡁⠀⠀⢹⡂⡗⣠⢒⠲⣍⠣⢱⢬⠩⣑⠡⠙⣧⠚⣥⢊⠷⣠⠃⠜⣠⠅⣫⢖⡹⡜⡝⢆⡀⠀⠀⠀⠀⠀⣴⠛⢄⠣⣙⠆⠰⡐⠬⠐⡀
⠀⠀⠀⠹⣎⠘⠠⠻⣜⠲⡝⣆⠒⡤⢧⠙⢆⠸⡳⣌⢳⡉⠆⠣⢀⡑⠎⣌⠛⠴⡩⢘⣣⠉⠖⣌⠲⣍⢎⠷⣩⠜⢢⠑⡶⠀⣀⠴⠚⡡⢌⡆⡱⠊⣌⡰⠃⠈⠒⠀
⠀⠀⠀⠀⠢⢍⠣⡱⠘⢯⠼⣸⠅⣿⢡⣋⠌⢧⡑⢚⢦⡐⠈⠐⠠⠑⡘⠈⠳⡄⠛⢤⡚⡙⢎⡐⣣⢎⠻⡜⠦⡑⢢⡙⢞⡩⢁⢦⡑⢃⠦⠙⠔⠉⠀⠁⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠈⠑⢡⡙⢄⠓⢆⠻⣄⠷⣈⣳⠈⡱⠌⢦⠑⡀⠀⠀⠀⠀⢠⢀⢣⠩⢄⠳⣙⠦⢸⡇⣌⡳⣍⡷⣍⠣⡑⢂⡌⣣⠆⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠏⣈⡱⢊⡼⣍⢧⡹⢄⡉⠲⣡⠐⠀⠀⢀⠀⡀⠉⠦⣍⠚⠴⣩⠓⡌⠉⡍⡱⢌⣲⢭⠛⣴⣫⣾⣷⣎⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⢍⠲⣬⡙⠳⣮⠑⣡⠐⣄⢆⣎⢦⡳⢌⡱⣘⠅⣮⡑⢧⡳⢈⠔⣤⡱⢏⡬⣍⢿⣸⢷⣻⣿⢾⣣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢪⡕⡤⢙⢣⡌⢙⡠⠘⠌⣌⠘⡡⢌⠭⢡⡉⢚⠱⢻⢧⡱⢩⡞⣥⠻⡍⠖⠋⠶⠩⣞⡱⢯⡟⡥⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⣸⢉⠶⣩⠎⡱⢆⡙⠦⣡⣉⡖⣤⢳⡴⢬⢴⣀⡒⣤⡉⡑⢎⠱⡛⢌⡡⢆⠀⠀⠀⠀⠀⣠⠙⣧⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠄⡀⡙⠠⢡⡞⣱⣊⠝⡪⠕⡯⡼⠶⣫⠜⠣⠶⡙⠔⣢⣙⡓⣮⢆⣱⢊⠱⣀⡚⡴⣒⣞⣱⠶⣉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣁⠞⡳⣜⡷⣎⢿⠗⣘⠰⠉⠘⢁⠫⡔⠁⠀⠠⢿⣽⠇⠹⡞⢻⣷⡎⠡⢰⠱⣙⢮⣟⡳⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠳⡌⣜⠱⣾⣿⢽⡂⢣⣤⣤⡄⡀⠀⠒⡠⢃⠀⠀⠀⡀⠀⠣⣌⢻⣽⣟⡆⣤⠓⡴⢢⠜⣡⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡹⢆⡙⣦⡿⣽⣻⠌⣴⣧⣟⡷⣿⡛⠄⠀⠀⢇⢎⡄⠰⢈⢡⠒⡈⠜⣺⢯⣿⣶⣯⡔⡉⢦⡑⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⠹⢯⡿⣽⡻⢴⠈⢋⣻⢙⡀⠁⠀⠀⠀⢨⠞⣬⠁⠆⢦⠑⡜⢠⣟⡿⣞⣷⡿⣽⠱⢂⡔⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠃⠱⠛⠂⠀⡁⢀⠈⠠⢉⡘⢀⢠⡘⣽⢆⡙⣌⠂⢡⠰⡁⡾⢹⡟⣾⡽⡱⡎⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠆⢮⣇⡜⢲⢍⡲⠿⣌⠓⡔⠠⡘⠄⡁⢆⢳⠀⠈⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⡤⢊⢥⢊⠥⣣⢌⢣⡜⢃⠰⡈⠝⣢⠙⢦⣀⡀⣤⠠⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠖⣀⠫⢄⢃⠞⡠⢊⠆⡘⠠⠂⢌⡑⢢⡑⢺⡔⠻⣆⡻⡌⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢜⢦⡙⠠⡐⡈⢄⠢⢁⠢⠄⠑⠤⠉⠤⢜⡣⢇⢢⢟⡱⣎⠡⢯⡹⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣞⡆⡈⢆⠡⡒⠦⡐⠢⠐⡈⠲⣀⠇⡖⣠⠒⡎⣵⠺⣕⢪⠃⣌⠱⣃⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣶⢩⠐⣬⢣⢑⡬⠑⠤⠁⠠⢱⠉⢾⡰⢁⠚⡌⢳⡹⢤⢃⡞⢠⠣⡌⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⣠⠇⢫⡖⢣⠎⣰⠋⠔⢨⢃⠃⢞⡁⢆⠣⡘⢌⡳⣹⠆⢹⢢⠇⣒⠡⢎⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢉⡰⠃⡌⡱⢋⢶⠀⠡⣎⡑⢢⡌⣙⢢⠘⣨⡑⡌⢢⣕⠫⡵⠈⠷⢮⣝⣓⡦⣅⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⡶⠁⠲⢄⠡⢎⡘⢬⣡⠠⢌⡑⢰⠌⣌⠲⢄⡘⢼⠣⣜⡳⢧⡑⠺⣱⠾⣥⢳⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠐⡡⢌⠐⡀⠀⠀⠀⠀⠀⢀⠇⣸⠇⢨⡱⢎⢳⡰⢈⠶⣠⠃⣦⠈⠇⣞⠠⣃⢬⡙⣦⡟⣶⣹⡟⢠⠡⣟⣳⢭⡳⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠰⣈⠐⠦⠑⡠⠀⠀⠀⠀⡎⢳⣚⣧⡠⣏⡽⣎⢷⣹⣎⡵⣞⣤⠿⣜⣢⢷⡜⣶⣻⡽⣿⠳⣽⣳⢂⡐⢬⢋⡾⠱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠄⠣⢄⠓⢄⠀⠀⠀⢸⣄⣢⣿⡜⣿⣽⣯⣽⣫⣷⣿⣻⣯⣿⣻⣾⢟⣿⣜⣷⡽⣿⣷⡿⣿⣿⣿⣷⡿⠘⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣽⢳⣿⠱⣯⡿⣽⣯⣟⣾⣯⣟⡿⣟⡿⣿⣟⡿⣯⣟⣾⣳⠿⢯⠿⢿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠈⠀⠙⣿⣻⣞⡿⣽⡾⣯⣿⡽⣻⣵⡻⣽⣳⣟⡾⣽⠘⡤⠚⢄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣯⣟⡾⣽⣻⢧⣟⣳⣯⡿⣽⣳⣿⢾⡟⣿⣌⣂⠱⣈⠘⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣏⣿⣳⣯⣟⡿⠉⠈⠁⠉⣟⡾⣯⢿⣿⡻⠀⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡞⣷⣽⣾⢧⡃⠀⠀⠀⢼⣹⢯⣿⢿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⡷⢋⢏⡐⠀⠀⠀⠮⡝⠿⡛⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣆⠺⡄⠀⠀⢀⡞⢡⢢⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡈⠄⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣌⠳⠥⠀⠀⠐⡬⢆⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡤⢋⡜⠂⠀⠘⣥⢈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢶⠉⡞⠀⠀⢠⢳⢈⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀