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