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