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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠄⡠⢀⠄⡠⢀⠄⠠⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢄⠰⢀⠆⡡⢂⡱⣈⢦⠱⣌⢦⡱⣌⢬⡑⢆⡒⠤⣁⢂⠐⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⡈⡔⢌⠢⡜⡤⣎⣵⣯⣶⣿⣾⣿⡾⣷⢿⡾⣧⣿⣮⣗⣧⡲⣌⡒⣄⠢⡈⠔⡀⢂⠐⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⣠⠚⡰⢡⣎⣷⣽⣿⣿⡿⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠑⢫⡞⡵⣋⠷⡙⢦⢳⡜⡤⡑⠢⢌⡐⠠⢁⠠⠀⢠⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠰⣀⢋⢤⣳⣽⣿⣿⣿⣿⠟⢡⡀⢆⡔⢡⠈⠄⠀⠀⠀⠀⠀⢸⣷⣛⢶⡱⢢⠍⡂⠆⡈⠱⠩⢳⠤⣌⠱⣀⠆⡏⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠆⡰⢑⡤⣯⣾⣿⣿⢿⣻⡿⢁⣎⡶⣽⢋⠜⠂⠄⠀⠀⠀⠀⠀⠀⠘⠛⠉⠉⢁⠋⠌⡑⢂⠰⢁⠒⢢⠋⠘⠳⡜⠛⡀⠁⠀⡀⠂⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⢠⡘⢴⣫⣾⣿⡿⡟⠞⢫⡟⢡⢎⡼⡝⢢⠁⢊⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢌⠠⡉⡜⣑⠚⠲⠡⠞⠁⠒⡔⠐⡈⠐⠀⠀⡐⢄⠂⠀⠈⠀
⠀⠀⠀⠀⠀⠠⠈⠠⡁⠜⢢⡼⣿⠿⠛⢉⠠⣐⡬⠉⠀⠀⠈⡐⠉⠂⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣶⣷⡥⣾⣣⡙⠤⡑⠢⠐⠀⢀⠢⠁⠂⠀⣮⠑⡌⠄⡁⠀⠀
⠀⠀⠀⠀⠀⠄⢂⠡⡘⢌⠷⠋⢁⣤⢶⣞⣿⣿⣿⠀⠀⢈⠻⡝⢒⠠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣞⡷⣓⢦⡙⢣⡄⢡⠠⣉⠇⡀⠂⢀⠐⠨⢳⢌⠒⠠⠀⠀
⠀⠀⠀⠀⠀⡐⠠⢂⠑⣨⣴⡾⣟⢾⣋⠞⣹⣞⡿⡆⠀⠀⠤⠐⠋⠁⠉⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠯⣿⣹⠖⣭⢒⡜⢤⡛⢁⠈⠀⠀⠄⠠⠀⠱⢪⡑⠌⡐⠀
⠀⠀⠀⠀⠀⠄⡡⢆⣿⡟⣧⡛⣵⢺⡔⣮⢱⣊⣿⡅⡄⠀⠀⠀⠤⣤⠀⠄⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⡟⣲⢯⡜⣦⢃⠀⠀⣄⠃⠌⠠⠐⠀⠳⣘⠰⢀⠀
⠀⠀⠀⠀⠌⢢⠑⣮⠷⢚⡔⡻⠈⢦⠙⣀⠣⡙⢮⠇⣿⠀⠀⠀⠀⠀⠁⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠘⠻⡇⠀⢀⡞⡤⢊⡔⢁⠠⠀⠱⣌⠒⡄⠂
⠀⠀⠀⠌⠰⡁⢞⣼⢋⠔⠈⠁⠜⢂⠰⢀⠲⣉⠎⣧⢻⠀⠀⠀⠀⠀⠈⠑⠀⢀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡝⠀⠀⠊⠝⡳⠃⠐⡂⠄⠐⠀⣎⠱⢠⠁
⠀⠀⠀⠌⣂⠱⢪⣽⠂⠀⠁⠈⠀⠀⠂⠈⢡⠘⡜⢦⢛⡄⠀⠀⠀⠀⠀⠄⠀⠢⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠘⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⢁⢂⠈⡀⠰⣌⠳⢠⠈
⠀⠀⠈⡔⢠⢉⢧⣻⠄⠀⠀⠀⠀⠀⠀⡁⠂⠌⡘⠤⢋⢦⠀⡂⠀⠀⢈⠆⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⡀⢄⡞⠀⢀⡠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⠲⡀⢂
⠀⠀⠐⡀⠆⡌⢲⡽⡂⠀⠀⠀⠀⠀⠁⠠⠈⠐⠠⡑⢌⣚⠀⡇⠀⠀⢬⡘⠁⠀⠀⠡⠀⠀⠀⠀⠀⠀⠀⠀⠄⠂⢠⠞⠀⠀⠲⣙⡆⠀⠀⠀⠀⠀⠀⠡⠈⢐⢊⠒⡁⠄
⠀⠀⠐⠠⠘⡠⢃⡞⣇⠀⠀⠀⠀⠀⠀⠀⠐⠈⠄⡐⣈⢾⠀⠀⠀⠐⢂⠀⡀⠡⠀⢐⡀⠀⠀⠀⠀⠀⠀⢀⠐⢠⠋⠀⠀⠀⣁⠒⠀⠄⠀⠀⠀⠀⠀⠐⠀⠏⢎⡁⢂⠐
⠀⠀⠀⡁⠂⠱⠨⣜⡹⡄⠀⠀⠀⠀⠀⠀⠐⠀⠠⠠⡱⠞⠀⠀⠀⠘⠀⠐⡈⢄⡉⡀⠄⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠐⠀⠂⡌⠀⠀⠀⠀⠀⠠⢀⡹⢍⡒⠌⣀⠂
⠀⠀⠀⢀⠡⠈⡅⢢⠝⣱⡀⠀⠀⠀⠀⢈⠀⠂⢀⠁⢴⠋⠀⠀⠀⠀⠀⠀⠈⢀⠰⠜⢤⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⢈⠒⡄⢀⠀⠀⠀⠀⠀⢄⠻⡜⢌⠐⡀⠀
⠀⠀⠀⠀⠠⠁⡄⠃⡜⣡⢷⡀⠀⠀⠀⠀⠐⠠⠀⣌⡎⠀⢀⢠⠐⡀⢂⡀⠀⠀⠠⠦⠀⠑⠄⠀⠀⠀⢀⠂⠀⠀⠀⠀⠀⠀⠠⢩⠔⠂⠀⠀⠀⠀⠀⡈⠷⣈⠆⢂⠀⠀
⠀⠀⠀⠈⠀⠡⣀⠣⢐⠡⡞⣹⢆⡀⠁⠠⢈⠐⡰⢦⣁⡎⢌⠒⡉⢀⠁⠀⠀⠀⠀⠀⠀⠄⠈⠐⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⡜⠀⠀⠀⠀⠀⠀⢀⠳⡐⢈⠀⢀⠀
⠀⠀⠀⠀⠀⠁⠄⠂⡌⢢⠙⣬⢛⢦⣅⠢⢌⢼⡹⠏⡰⠈⠄⠃⠤⢈⠈⠁⠀⠀⠀⠀⠀⠀⠁⠂⡀⠈⢤⠀⠀⠀⠀⠀⠀⠀⠐⡨⢄⠠⠀⠀⠀⠀⠀⠀⠣⢁⠂⠄⠀⠠
⠀⠀⠀⠀⠀⠐⢈⡐⠨⠄⡋⢤⢋⡖⢮⢷⡾⠎⠐⠀⠁⣀⠀⠁⠀⠂⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⡙⠖⡆⡄⢀⠀⠀⡀⡑⡀⢀⠀⠀⠀⠀⠀⠀⠐⠠⢈⠀⠠⠁
⠀⠀⠀⠀⠀⠀⠂⠄⢡⠂⣉⠦⣩⠼⣭⡟⠡⠈⠀⠀⠀⠈⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⡐⠈⢒⠉⠎⢎⠑⠲⠁⠐⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⠠⠀⠀
⠀⠀⠀⠀⠀⠀⠡⢈⠄⡘⢄⡊⡔⠹⠁⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠀⠀⠀⠀⠀⠀⢀⠐⠈⢀⠁⠂⠈⠄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⠀⢀
⠀⠀⠀⠄⠀⠀⠀⠈⠢⡑⢂⡐⠈⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⠀⢀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠠⠈⡀⠂
⠀⠀⠀⠈⠰⢀⠀⠁⡐⢈⠡⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⡐⠠⠀⠀
⠀⠀⠀⠀⠀⠈⠢⡁⠀⠄⠠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⠀⠀⠀
⠀⠀⠀⠀⠀⠁⢂⡈⠡⠌⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠈⠒⡄⠠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠁⠄⡐⠈⠁⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀