Christmas tree Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠀⠀⠀⠀⠀⠀⠀⢀⣘⣛⣂⠀⠀⠀⠀⠀⠀⠀⠀⣰⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⢁⡿⠄⠀⠀⠀⠀⠀⠈⠙⠛⠉⠀⠀⠀⠀⠀⠀⠀⣰⣿⢿⣧⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⢀
⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠙⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣹⢸⡟⣇⠀⠀⠀⠀⠀⠀⡀⠀⠉⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠀⠀⡍⠰⠀⠀⠀⠀⠀⠴⣠⠄⡧⣠⠀⠀⠀⠀⣰⢻⡇⣿⢸⡇⢹⡄⠀⠀⠀⠐⠀⠀⠀⠆⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢀⣬⠭⠵⣫⡴⣿⡂⠀⠀⣠⠇⡾⢸⣿⢸⣿⠈⢷⡀⠀⠀⠐⠀⠁⠀⠖⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠐⠚⠋⠥⠞⠑⠃⠀⠀⠉⠈⠁⠉⠉⠈⠉⠀⠈⠁
⠀⠀⠀⢰
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠸
⠀⠀⠀⢸
⠀⠀⠀⠈⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠸⠇⠀⠀⠀⠀⠀⠀⠀⢸⡃⠀⠀⠀⠀⠀⠀⠀⢽⠀⠀⠀⠀⠀⠀⠀⠐⠃
⠀⠀⠀⠀⠀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠆⠃⠐⢩⢔⠀⠀⠀⠀⠀⠚⠥⠀⠀⠀⠀⠀⠀⢠⢋⡂⠀⠀⠀⠀⠀⠀⠄⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⠀⡔⠃⢒⡀⠀⠀⠀⠀⡈⠉⠭⠂⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠐⠠⠠
⠀⠀⠀⠀⠄⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆⠃⠀⡈⠀⠰⠣⠀⠀⡀⠭⠭⠭⠙⠀⠀⠀⠀⢸⠗⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠄⠉⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠈⠋⠉⠌⠄⡠⠀⠀⢑⣒⣒⢒⣒⣲⠄⠀⠀⠍⠀⠀⠀⠀⡄⠀⠀⡄⠀⡀
⠀⠀⠀⠀⠈⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠠⠌⠌⠀⠀⠀⠀⠀⠀⠸⠡⠤⠬⡭⠥⠤⠄⠀⠐⠦⠀⢀⠀⠀⠀⠀⠀⠀⠁⣀⡐⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠐⠒⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣼⣿⣁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣨⣿⠋⣥⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢯⣿⣿⣿⣷⣫⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣶⡈⣻⣿⡟⠛⠫⣥
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⡾⢿⡏⢙⣧⣀⣴⠛⢋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣶⡀⢀⣿⠟⢿⡟⠛⣶⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠻⣿⡿⢿⣿⣾⣿⡿⠿⢿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⣿⣏⠀⠀⣿⣄⣼⣇⠀⣀⡟⣃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠋⠉⢹⣿⡿⣿⡿⠛⠻⣿⣿⠿⢿⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⣦⣤⣼⣷⣴⣿⣇⠀⣀⣿⣧⣤⣾⣭⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡻⠛⣿⣿⠛⠛⢻⣿⠟⠿⣿⣧⣽⣿⡏⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣷⣴⣿⣿⣄⣀⣸⣿⣤⣤⣿⡟⠉⠹⣿⡿⢻⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⡿⠛⢿⣿⡿⢻⣿⣿⣿⣧⣤⣶⠿⠿⢿⣛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣀⣀⣼⣷⣤⣼⣿⣿⣿⣿⣧⣀⣿⣿⣏⡀⠀⣼⣿⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠿⣟⠋⢻⣿⢉⣻⡏⠀⠈⢻⣿⣿⠋⢹⣿⣿⣾⣿⠟⠳⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣷⡿⣿⣿⣿⣿⣿⣿⣷⣦⣴⣾⣿⣿⣿⣿⣿⣤⣾⣿⣦⣶⡷⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⣷⣍⣀⣸⣿⠁⠀⢹⣿⠛⠛⣿⣿⣥⣿⡟⠁⠉⢿⣏⠁⠹⣟⠛⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠩⠭⣿⣿⣿⣿⣦⣴⡿⢻⣶⣾⣿⠋⢹⣿⣧⣄⣠⣿⣿⣿⣿⣿⣿⣿⣟⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠛⣛⣿⣿⠿⢿⣶⣾⠿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠉⠁⠀⠀⠉⠁⠀⠈⠉⠉⠉⠉⠁⠉⢫⠝⠛⠀⠉⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡌⠀⠀⠀⠀⠄⠀⢤⣄⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠠⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠉⠐⠤⠀⠤⣄⠠⠀⠀⠉⠀⠀⠀⠀⠀⠀⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠁⠈⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠁

⣿⢿⠿⠿⡿⡻⠿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣧⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣧⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⡿⣋⣴⠾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣩⣾⣿⣿⣿⡿⠋⣁⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⢟⣩⣶⣿⠟⣉⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠟⣫⣾⣿⠞⣫⠿⣫⣴⡿⢛⣡⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡾⠟⣉⣴⣿⣿⡿⢟⣭⣶⡿⠋⣀⣴⣶⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠟⢉⣴⣾⣿⣿⣿⡿⢞⡿⠟⣩⣴⣿⠿⠋⣀⣴⣶⢂⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁⠀⠾⢛⣽⣾⠿⢛⣥⢞⣫⣶⣿⠿⢋⣡⣶⡿⠿⠿⠿⡿⠛⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢋⣤⣾⣿⡿⣿⣿⣿⣵⣾⠿⣋⣥⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⠿⣋⣵⣾⠟⣫⣿⣿⣵⡾⠛⠉⢀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⡿⠟⢉⣴⡾⠟⣩⣴⣿⣿⠿⠛⠁⣀⡴⠞⢋⣡⣴⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠿⠋⢁⣤⡾⠛⣉⣴⣾⣿⠿⠋⢁⣠⡶⠟⣉⣤⣾⡿⠟⣁⣤⣶⣦⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡶⠛⢁⣴⣾⣿⠿⠋⣁⣴⠾⢛⣡⡴⢛⣽⢞⣫⣶⣿⣿⣿⣿⢛⣿⣧⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠁⣤⣾⣿⠿⢋⣡⣶⠟⣋⣥⠾⣋⣵⣾⣿⣿⣿⣿⣿⣿⣿⡟⠋⡛⠛⠃⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⣋⣥⡾⠟⣫⡴⠞⣉⣴⣾⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣾⣏⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣵⡾⢛⣭⠶⠛⣡⣴⣿⣿⣿⣿⣿⡿⣟⣯⣷⣿⣿⣿⣿⣿⡿⣟⣽⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡿⣛⣵⠞⢋⣠⣶⣿⣿⣿⣿⣿⢟⣫⣵⣾⣿⣿⣿⣿⣿⢟⣫⣵⣿⣿⣿⣿⣿⣇⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⡿⠛⢉⣠⣶⣿⣿⣿⣿⣿⢟⣭⣶⣿⣿⣿⣿⣿⡿⢛⣩⣶⣿⣿⣿⡿⣿⣿⣿⣿⠿⣿⡇⢀⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠟⠋⢁⣠⣶⣿⣿⣿⣿⣿⣿⣿⣾⢿⣿⣿⣿⣿⠟⣋⣵⣾⣿⣿⣿⠿⣛⣭⣾⣿⠿⢛⣥⢞⣭⠶⣿⣅
⠀⠀⠀⠀⠀⠀⠸⠟⠉⠀⢀⣶⣿⣿⣿⣿⣿⣿⣿⣿⣻⣽⣾⣿⡿⢛⣩⣴⣿⣿⣿⣿⠟⣫⣵⣾⣿⠟⢋⣡⣾⣿⣿⣿⣿⣿⡿⠛⠿⠷⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣟⣯⣷⣿⣿⠿⣋⣥⣶⣿⣿⣿⡿⢟⣫⣶⣿⡿⠟⢋⣤⣾⣿⣿⣿⣿⣿⣿⠿⠋⣀⣀⣀
⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⣫⣴⣾⣿⣿⣿⡿⣛⣽⣾⣿⡿⠛⣉⣴⣾⣿⣿⣿⣿⣿⣿⡿⣛⣥⣾⣿⣿⣿⣯⡀
⠀⠀⠀⢀⣠⡶⣛⣿⣿⣿⣿⣿⣿⣿⡿⢟⣩⣶⣿⣿⣿⣿⡿⣻⣵⣾⣿⠿⢋⣡⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⡿⢋⣤⠀⣠⡄
⠀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣷⣿⡿⠟⢋⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣻⣿⣿⣾⣯⣵⡾⣋⣤⡶
⣸⣿⣿⣿⣿⣿⣿⠿⠛⢿⣿⣿⣯⣷⣿⣿⣿⣿⣿⣿⠿⠛⣁⣤⣾⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⣵⣾⣿⣿⠟⣫⣿⣿⣿⣿⣻⡷⠻⣆⣠
⠉⠛⠉⠛⠁⠉⠁⠀⠀⠘⠋⢩⣽⣿⣿⣿⡿⠟⢋⣡⣴⣿⣿⣿⣿⣿⣿⠿⢛⣩⣾⣿⣿⣿⣿⣿⣿⣿⠻⣿⣛⣠⣾⠟⣉⣴⣾⣿⣿⣿⢛⡿⠛⠁⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠿⠟⠉⠀⠘⢋⡽⢿⣿⡿⠿⠛⢋⣡⣶⣿⣿⣿⠟⠉⠉⠋⠙⠛⠉⠃⠺⠏⠀⠀⠀⠉⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠐⣿⣿⠿⣿⠟⠁⣠⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⣡⣞⣥⣶⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⢋⡵⢋⣤⣶⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠞⠋⣼⣷⡄
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣶⣶⣶⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⣿⣿⣿⣻⣿⣿⡿⣿⣿⢻⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠀⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⢀⡀⣿⣿⣴⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⢿⡿⣿⣿⣿⣟⡳⣤⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠋⠀⠀⣯⣿⣿⣿⣿⣋⣀⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⣿⣶⣶⣿⣿⣿⣿⣿⠿⠛⠉⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⠛⠻⣿⡿⠻⢿⣿⣅⡀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⡿⠿⡀⣴⣿⣿⣿⣿⡟⢿⣿⠻⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣄⣰⣆⣡⣾⣿⣿⣿⣿⣿⣿⡟⠦⠙⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣮⣿⣿⣿⣿⣿⣿⣧⣽⣿⡛⢿⡿⣷⣶⣶⣦⣤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢩⣍⡉⠉⢠⣷⣬⣾⣿⣾⣿⣤⣦⣿⣿⣿⣯⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⣽⢿⢷⣈⣤⣽⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣴⣶⡶⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣷⣾⣿⣿⢿⠿⡟⢷⣾⢿⣿⣿⣿⢿⣿⣷⣛⠿⢿⣾⣅⢶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣽⣿⢟⡀⢀⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣦⣈⠉⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣦⣜⠛⠉⣱⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⡿⡏⠉⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣀⣝⣿⣿⣶⣿⣯⣽⣿⣿⣿⣿⠟⢿⣿⣏⣽⣿⣬⣛⣻⣿⡿⣿⣶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣴⣿⣿⣿⣿⣿⣟⣻⣿⠏⠛⠻⠇⠙⠃
⠀⠀⠀⠀⠀⠀⢀⣴⣶⣾⣿⣿⣿⠿⠻⣿⣿⣩⣿⣿⣿⣿⣿⣿⣿⡟⠫⠈⠁⣿⣿⣿⣿⣶⣿⣶⠖
⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠛⣿⣷⣤⣼⣾⣿⣿⡿⠋⣻⣿⣿⣿⣿⣇⣰⠀⢀⣿⣿⣿⣽⠙⠿⣿⣶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠟⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣦⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢿⣿⡻⣿⣿⠿⢿⣿⠏⠹⣿⣿⣿⣏⠛⠻⣿⡷⠉⠙⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠙⠋⠀⠀⠉⠀⠀⠀⠀⠙⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⠀⠀⠀⠀⢠⠀⢀⠀⠀⠀⠀⠀⡀⠀⡀⠀⢀⠀⠀⠀⢠⠀⡄⢠⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠀⠀⠀⠀⠈⠀⠈⠀⠀⠀⠀⠀⠁⠀⠁⠀⠀⠁⠀⠀⠀⠁⠁⠈⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢰⡆⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣌⣱⠎⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⢤⣿⣷⡶⢀⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⠞⠛⢁⣄⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣦⣤⣶⣾⢹⡅⣠⠶⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢡⡿⣧⣾⣷⣤⠆⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣤⣄⡋⣀⡿⠿⠛⢠⣼⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⢉⣁⣅⣠⠄⢾⠿⠾⠂⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⠏⠈⢻⣄⣘⣷⠈⠑⠲⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⠠⣤⠟⠁⡈⣠⡴⠋⠉⡾⠆⡷⠂⣈⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⢂⣾⣿⠋⡪⣴⣀⢱⡤⠶⢂⣤⣩⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢆⣄⠴⠲⠾⠿⢃⢠⣄⣼⠛⠋⡀⠐⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠄⢠⡶⢠⣀⣈⣉⠀⠴⠶⡅⠀⣀⡤⢠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⣠⠘⡻⠊⣸⡿⠃⠀⠘⠋⠀⠀⡈⠁⠀⢀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⠀⡀⣤⡂⠀⠈⠀⢸⡿⢁⠠⣀⠖⠀⠀⠀⠈⠓⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠁⠀⠀⠐⣿⣾⠋⠀⠉⠀⢠⠀⠀⠈⠰⠄⣠⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠂⠀⣄⠀⢀⠀⠄⢻⣿⣶⡀⠀⡰⢿⠀⢀⢀⠄⠂⠠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⢤⠀⠈⠁⠀⠀⡰⠃⠀⠀⢀⣧⡀⠀⠀⠦⠈⡀⠰⠊⠀⠀⡀⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠸⠄⠀⠀⠀⠉⠒⠥⠰⠚⠃⠐⠒⠀⠚⠛⠟⢉⣠⠤⠊⡑⢈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁⠂⠐⠂⠀⠂⠠⣤⣦⠔⠀⠀⠹⠷⡰⠚⠓⠋⠀⠀⠀⠀⠀⢀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⢤⡀⠀⠀⠀⠀⠀⣤⣄⣀⠆⠚⢸⣿⠏⠀⠀⠀⣶⡆⠀⢈⡀⠀⠀⠒⢀⡀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠄⣨⡼⠏⠀⠀⡸⢡⠀⣀⣠⠁⠀⠀⠀⠀⠘⢆⠀⢀⠀⠈⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠋⠀⠀⠀⠀⠁⣿⣿⣿⡇⠀⢠⡈⠀⢀⠀⠈⠡⠀⠈⠀⠐⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠻⠝⣿⠁⠐⠈⠁⠀⠀⠃⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠘
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢙⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠙⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣾⣾⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⠙⠀⢈⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⡋⣳⡄⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠰⡦⠹⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢈⣟⠛⣿⣿⣿⣏⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠆⣤⡄⠀⡀⠀⣾⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⡏⢹⣧⡀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣯⡷⠁⠤⠀⠀⠀⢰⣿⠎⢿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠉⠉⠉⠉⣿⡏⠉⠉⠉⠁⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠆⠀⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣼⣇⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⣷⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣿⡟⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠘⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠁⠀⠀⠈⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⡶⣤⣤⣴⣤⡾⠷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣷⠀⠀⠀⠀⣼⣋⣻⠀⠙⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣯⡤⠉⣗⡆⠀⠀⠈⠉⠉⠀⠀⢤⣵⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠙⡶⢠⡾⠿⣷⣀⡀⠀⠀⠀⠀⢞⠃⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠛⠛⠉⠛⢷⡤⡄⠀⠀⠈⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⣽⣿⣿⢦⣴⣄⡱⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠶⠏⠀⣽⠿⢿⠉⠑⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⣶⡧⣤⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⢿⡤⢸⣶⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣖⡿⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋⠀⠀⠀⠀⠀⠀⣀⡀⣀⡤⣤⣴⣲⠖⠻⣾⠿⢯⠀⠀⠱⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⠭⠗⣾⣽⣶⣿⠽⠛⠓⠋⠉⢹⣯⣿⡆⠀⠀⠙⠛⠋⠀⣀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣎⣥⣆⣴⢞⣁⣻⣭⣽⠀⠀⠀⠀⠀⠈⠛⠋⠀⠀⠀⠀⠀⠀⣀⣈⠳⣤⣶⣌⣳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠋⣩⡿⣅⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣉⠛⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡾⠋⠉⠉⠛⣽⣶⣖⣦⣠⢤⡀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠻⢿⠇⠀⠀⠀⠘⣿⣭⡏⠀⢈⣿⣻⡷⠛⠻⣽⣶⣟⠦⢴⣲⠤⣖⠶⠾⡿⠦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠟⢲⣾⣵⣧⡶⠃⠀⠀⠀⠀⠀⠀⠀⠈⠳⠾⠃⠀⠘⣯⣭⠇⠀⠀⠀⠀⠙⣦⣴⣾⣷⠚⠳⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⡤⣀⣴⣺⠧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⢟⣶⣶⣖⣦⣤⢲⣤⣴⣢⣤⣖⣦⠴⣲⠶⠾⣽⡿⣷⠛⠉⠛⠁⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠶⠗⢲⠿⣿⣪⣿⣾⠇⠉⠀⠨⣿⣙⡧⠀⠀⠀⠀⠀⠻⣶⠿⠀⠀⠀⠀⠐⢿⡾⢿⡖⠽⢦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⣯⣿⢿⣲⣤⣠⢤⡙⣋⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠋⠁⠉⠀⠋⠀⣽⡯⣿⠊⠉⠓⠛⠛⢯⡿⣾⡽⠶⢾⡷⠶⢏⣶⣶⡭⠖⠺⠽⠓⢦⡀
⠀⠀⠀⠀⠀⠀⢀⣠⣴⣊⢥⡶⠃⠀⠀⢀⡴⣤⢈⡟⣻⠀⣠⡄⢠⠿⣸⣯⣿⡁⣠⣄⢰⡄⣴⣯⣬⣧⡀⠀⠀⠙⢶⠬⣳⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠈⠉⠁⠰⠞⠒⢏⡤⠞⠹⠋⠱⠊⠷⠛⠋⠁⠈⡇⠀⠀⠀⢸⠋⠁⠈⠛⠙⠞⠻⠏⠻⠏⠲⢄⡟⠚⠳⠀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣀⠀⠀⠀⣀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉

⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⢠⠄⠀⠀⠀⠀⠀⢠⣆⠀⠀⠀⠀⠀⠀⠦⠀⠀⠀⠀⠀⠀⣴⣄⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠐⠂
⠀⠀⠀⠀⣰⣣⡄⠀⠀⠀⢀⣼⣿⠀⠀⠀⠀⠘⣣⠒⠀⠀⠀⠀⢾⣿⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡄⠀⠀⠀⠀⣴⣶
⠀⠀⠀⢠⡯⠏⠁⡀⠀⠀⠸⢿⡿⠇⠀⠀⠀⠠⠰⠀⠀⠀⠀⠴⣿⣿⡷⠄⠀⠀⠀⠀⠀⠀⡂⠀⠀⢀⣾⣿⣿⣧⡀⠀⠀⠀⣷⣿⣆
⠀⠀⠀⠚⠉⠙⠛⠛⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠈⠘⠉⠉⠉⠁⠀⠀⠀⠀⠂
⠀⠀⠀⠀⢀⣴⡀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⢀⣆⠀⠀⠀⠀⠀⠀⣼⡄⠀⠀⠀⠀⠀⢀⣇⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⣸⡀
⠀⠀⠀⢀⣼⣿⣧⠀⠀⠀⢀⠡⠀⠀⠀⠀⠀⣼⣿⡄⠀⠀⠀⢠⣾⣿⣦⠀⠀⠀⠀⢾⣿⣿⡂⠀⠀⠀⢀⣽⣿⣄⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⣴⣿⣿⡄
⠀⠀⠀⣠⣾⣿⣷⣄⠀⠀⠈⠐⠀⠀⠀⠀⢠⣾⣿⣦⠀⠀⠀⣴⣿⣿⣷⡄⠀⠀⠰⣿⣿⣿⡦⠀⠀⠀⣠⣾⣿⣧⠀⠀⠀⠀⠄⠀⠀⠀⠀⠘⣿⣿⣿⡷
⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠙⠙⠋⠁
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣏⣀⣉⣈⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣧⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠛⡿⠆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡟⣄⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⢯⣄⠈⢷⣜⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⢫⣿⣾⠁⢳⣄⠻⡷⣝⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⣱⣿⣿⡟⢲⡀⠻⣧⡈⢮⡳⣝⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⡿⢃⣼⣻⣿⡟⣇⠀⠹⣦⡈⢯⡢⣙⢦⡑⢽⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⢟⡽⢋⣴⡟⣱⣿⠟⣴⡏⢷⣄⠈⠻⣦⡙⢮⡓⢭⣢⣌⠛⠿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣩⠖⢋⣴⣿⢋⣼⣿⢋⣾⠳⡇⠀⠹⣷⢄⠙⢿⡳⣽⣦⡈⠛⠷⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠵⠚⣩⠞⣡⣾⠟⣡⣿⠃⢠⡟⢦⡀⠈⠳⡙⢦⣙⢦⣉⠻⢶⣄⡀⠉⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⣡⢾⡿⣫⡾⡿⠃⣠⢿⣦⡀⠻⣦⡀⠙⢦⡈⠓⢬⡳⢤⡈⠛⠳⢶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⠿⠛⣱⣟⡴⣫⠞⢁⣼⠟⢸⡏⠻⣦⡈⠻⣷⣄⡙⠦⣀⠈⠑⠻⢷⣤⣀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⢋⡴⠃⣴⣿⠋⣰⢻⠷⣄⠙⢿⣷⣌⠻⣝⠲⣬⡳⢤⡀⠀⠀⠉⠙⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠛⢁⡴⠋⣠⣾⠟⢡⣾⠏⣸⠧⣜⢷⣄⡙⠻⣟⢮⣝⣦⣍⠓⠿⣷⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠉⢀⡴⣋⡴⣚⡿⢁⡴⣫⢏⡼⢻⠀⠈⠳⣝⢿⡦⣌⠙⠮⣙⠻⢿⣶⣤⣉⡙⠛⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠟⠛⣡⠖⢋⡴⢋⡜⣡⠞⠁⢸⠀⠀⠀⠈⠓⢿⣮⣝⠲⠮⣽⣶⣄⡉⠙⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢚⣡⠖⢋⡴⢋⡾⠁⠀⠀⢸⠀⠀⠀⠀⠀⠀⠈⠛⠷⣦⣄⡈⠉⠙⠛⠶⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡾⠿⠚⠉⢀⡴⢋⡴⠋⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠲⠦⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢋⡴⠋⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣫⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉

⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤
⠀⠀⠀⠀⠀⣹⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⣗⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣿⡄
⠀⠀⠀⠀⢀⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡿⢀⠀⠀⠀⠀⠀⠀⠀⠀⡄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⢛⣿⣿⣟⠦
⠀⠀⠀⠀⣸⣯⣿⣧⠀⠀⠀⠀⠀⠀⢴⣶⣾⣶⣿⢿⡇⠀⠀⠀⠀⠀⠀⠀⣠⠐⠂⢁⠀⠀⠀⠀⠀⠀⢾⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⣠⣾⣯⣿⣟⣆⡀
⠀⠀⠀⢰⣿⣿⣿⣿⡆⠀⠀⠀⠀⢠⣶⣷⣶⣷⣶⣿⣿⡆⠀⠀⠀⠀⠀⠂⠠⢀⡀⠀⠀⠀⠀⠀⠀⢴⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠈⠉⣽⣿⣿⣿⣿⠛⠄
⠀⠀⢀⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⣬⣟⣛⣛⣛⣫⣭⣾⣿⡆⠀⠀⠀⠉⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⣰⣿⣿⣿⣿⡆⠀⠀⠀⠀⢀⣤⣿⣾⣿⣿⣿⣿⣇⡀
⠀⠀⠈⠉⠉⠹⠿⠉⠛⠃⠀⠀⠀⠉⠈⠛⠋⠿⠋⠈⠉⠈⠁⠀⠀⠈⠀⠀⢠⣤⠀⠀⠀⠀⠀⠀⠀⠉⠉⠹⠏⠉⠉⠀⠀⠀⠀⠈⠉⠈⠉⠹⠟⠛⠿⠿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠰⠀⠀⢠⡄⠀⠀⠀⠀⠰⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡄
⠀⠀⠀⠀⠀⠠⠋⠁⠀⠀⠀⠀⠞⣿⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠆⠀⠀⢠⣿⣄⠀⠀⠀⠀⠀⠀⠰⠆⠀⢀⣦⡀
⠀⠀⠀⠀⠀⠉⣶⠶⠁⠀⠀⢀⠾⣿⠣⡀⠀⠀⠀⢀⣾⡄⠀⠀⠀⣹⡅⠀⠀⢩⣿⡄⠀⠀⠀⢀⡀⠀⠀⠀⠀⣹⣿⣏⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⢀⡼⣿⢷⡈⠀⠀⢀⣾⣿⣿⡀⠀⢈⠼⢌⠀⠐⢛⣿⡟⠀⠀⠀⣼⣧⠀⠀⠀⠉⣹⣿⣏⣉⡀
⠀⠀⠀⠀⠀⠘⠉⠁⠀⠀⠀⢈⡴⣿⣧⡙⠂⠀⣾⣿⣿⣿⣷⠀⡨⢘⠢⡁⢠⣾⣿⣿⡆⠀⢠⡿⢼⡄⠀⠀⢙⣿⣿⣏⣉⣀
⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢉⡴⢿⢦⠑⠆⣸⣿⣿⣿⣿⣿⣧⠠⠞⠦⠀⠈⣸⣿⣆⠀⠀⣾⡿⢹⣷⠀⠲⠟⣻⣿⣿⣭⣄⡀
⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠐⠋⠀⢸⠀⠑⠀⠟⠿⠿⠿⠻⠟⠛⠂⢸⠀⠀⠼⠿⠿⠿⠇⣸⣿⣧⣽⣿⡆⠠⡾⠿⣿⢿⣧⣀
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠈⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣷⣯⣿⣛⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣻⣿⣿⣿⣿⡋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣟⡿⣿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⣿⣿⣿⣿⣷⣾⣯⣽⣿⣧⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠶⣿⣷⣽⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣷⣽⣛⡿⢿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣮⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⣾⣿⣿⣿⣿⣿⣷⣯⣿⣻⣿⠿⠿⠿⠿⠿⢿⣿⣛⣂⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⠿⢿⣿⣿⠿⢿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⠀⠀⠀⠙⠛⠀⠀⠀⠉⠉⠉⠉⠉


⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣟⣛⣟⣛⣻⣟⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢠⣀⣿⣏⠀⡀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢦⡈⢿⣿⣿⣶⣤⠾⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣹⣷⣽⣿⣯⣴⢛⢀⡀⠃⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣴⡾⠿⣿⣿⣗⠉⠉⠛⠛⠉⢩⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⢶⣍⣯⠀⢀⢽⣿⡿⠦⠄⣁⣀⠀⠛⠃⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡠⣤⡄⠽⢻⣿⡷⣾⠟⠑⢰⣼⣿⣛⣤⡶⠯⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢙⠓⠓⢓⡋⠰⢿⣿⣿⣿⣿⣿⣿⣟⠛⠛⠛⠓⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠃⠀⣠⣄⠐⠏⣿⣿⡅⠀⠙⣿⣍⢁⣁⣈⣀⣤⢶⡾⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠢⠄⠀⠀⠒⢿⡿⠿⢷⣶⣽⡳⢦⠾⠿⢏⣿⣿⣭⣻⠍⠁⠀⢘
⠀⠀⠀⠀⠀⠀⠀⠉⠀⢂⣀⣩⣿⠀⠀⢰⣟⣿⣿⣿⣿⣷⣿⡛⠙⠻⠏⠈⣤⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠙⠛⠿⠿⠲⣿⣭⣿⣿⣿⢿⣝⣿⣟⣶⡴⠾⣻⠿⢷⠶⡦
⠀⠀⠀⠀⠀⠀⠰⢽⣦⣶⣶⣾⣴⣶⡿⠟⢿⣿⢀⣟⣶⣿⣿⣿⠁⠀⠀⡸⣦⠴
⠀⠀⠀⠀⠀⠀⠀⢠⣤⣠⡤⡀⣉⡐⣤⣥⡼⣟⣯⣿⣏⣳⣮⣿⣷⣀⣈⣽⣧⣶⣯⣭⣀
⠀⠀⠀⠀⠙⠗⣶⣦⣄⣉⡉⢁⣭⣍⣛⣷⣿⣿⣿⣬⣋⠻⡟⣿⣯⣹⣿⡷⣶⣤⣬⣍⠙⠓
⠀⠀⠀⠀⠈⠀⠀⣈⠹⠙⢙⣿⢿⣿⠋⠉⠉⢿⣿⣷⣿⣟⣧⣸⣽⣿⠿⢿⣞⣂⣉⣉⡀
⠀⠀⠀⠀⢀⣠⣤⡤⠶⠚⠋⢀⣽⣿⠀⢠⢄⣹⣿⣿⣿⣿⣯⣀⣼⡁⣀⠀⣿⣿⠿⢿⣢⣦⣤⡀
⠀⠀⠀⠈⠉⠀⠀⠀⢀⣠⣶⣿⣍⣿⡿⣛⣿⠻⣿⡿⡏⣿⣏⠿⣼⡿⢶⠾⠻⡷⠄⡀⠈⠉⠉⠁
⠀⠀⠀⡀⠀⠀⠀⠀⠙⠋⠉⠀⣉⣽⠿⠛⠁⣰⠟⠈⣷⡜⢿⣆⠀⠛⢷⡀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠁⠀⠀⠀⠀⠀⠀⢹⡧⠀⠈⠀⠀⠀⠘⠃
⠀⠀⠀⠀⠀⠀⠄⠀⠊⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠄⢀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⠀⣈⣏⣹⣋⣏⣫⣙⣏⣙⣉⣋⣟⣉⣉⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⣭⣿⣿⣯⣿⣟⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡽⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣻⣱⣂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣐⣻⢯⣏⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣡⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣟⡬⣷⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡲⠌⡀
⠀⠀⠀⠀⠀⠀⢰⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠼⣿⣿⣿⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣜⠲⠿⣿⠂
⠀⠀⠀⠀⠀⢠⠷⠀⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢚⣿⢻⡟⢚⠓⡖⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⡉⢖⣤⣛⡄
⠀⠀⠀⠀⠠⣌⡐⠂⠄⠫⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣻⣿⣰⣶⣿⣿⣉⠀⠀⠀⠀⠀⠀⠀⠀⠠⠬⠽⣃⢤⠨⣟⣂
⠀⠀⠀⢀⠒⠀⠠⠄⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣙⣿⣯⣿⣷⣾⠇⣀⠀⠀⠀⠀⠀⠀⠀⠲⢶⠺⠇⢘⠃⠙⡴⠖
⠀⠀⠀⡀⠑⠂⠄⠄⠒⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⢩⣟⣙⣿⣿⣿⣿⣿⣇⣀⠀⠀⠀⠀⠀⠀⠓⣎⣑⠋⡉⠐⠼⠗⣚
⠀⠀⠀⠃⠐⠀⠒⠒⠂⠀⠚⠁⠄⠀⠀⠀⠀⠀⢶⡖⣿⣟⡑⣿⣹⣆⣿⣏⣁⠄⠀⠀⠀⠀⢩⣎⡝⣿⠏⡽⡤⠘⢘⠥⡠⠄
⠀⠀⠁⠀⠀⠶⠀⡀⠁⠈⠉⠀⠀⠀⠀⠀⠀⣄⢀⢩⣽⣿⠿⢿⡿⣿⣿⣿⢃⡀⢀⠀⠀⠀⡑⡀⠀⡦⢰⣆⠀⢋⣴⣧
⠀⣌⠃⠄⠤⠀⠄⠀⠀⠂⠀⠁⠀⠡⠀⠀⠀⢀⠙⣫⣾⣯⣼⣿⣗⠛⣿⣟⡿⣟⠃⠀⢀⡺⢿⡓⢒⡂⣠⡄⢤⣤⡀⢩⣤⠀⡀
⠀⠀⠁⠀⠀⠀⠀⠂⠘⠐⠂⠀⠀⠀⠀⠀⠈⠉⠙⢻⣿⣧⢼⣿⠿⣿⣾⣦⠾⠗⠛⠀⠀⠉⠛⠁⠁⠷⠟⠃⠈⠈⠑⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠉⠓⠉⠉⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠋⠛⡛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⡍⠠⠀⠀⠀⠀⠀⠀⠀⢂⠀⠀⠀⠀⠅⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⣤⠠⠄⠀⠀⠀⠀⠀⠰⢽⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⠀⠀⠀⠀⠀⠀⠠⠫⢝⢔⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠎⠃⠂⠀⠀⠀⢤⣭⠦
⠀⠀⢰⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠠⢦⣤⠶⠂⠀⠀⠀⠈
⠀⠀⣾⣿⡀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣤⣤⡶⠞⠂
⠀⢸⣿⣿⣇⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢰⣦⣤⣤⣤⡶⠞
⢀⣿⣿⣿⣿⡄⠀⠐⠐⠀⠀⠐⠂⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⡀⠀⠀⠀⠀⠂
⠀⠉⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠀⠀⠈⠀⠀⢀⢁
⠀⠀⠀⠀⠀⠀⠀⣀⣐⡂⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⣈⣛⣁⠀⠀⠀⠠⢈⠠⠄⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⣙⣟⣁⡤⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⡀⠀⠀⠀⠀⠀⠀⠀⢀⣉⣻⣥⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠡⠠⠄⠀⠀⠀⠀⠀⠀⠀⠠⠀⠈⠹⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠠⠀⠀⠀⠀⠀⢁⢁⠁⠉⠄⠄⠀⠀⠀⠀⠐⡀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣺⣗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠂⠐⠐⠐⠈⠀⠀⠀⠀⢈⠀⠀⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠠⠟⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⢨⠀⠀⢀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠀⠀⠠⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⢀⠀⠂⠐⠒⠀⠀⠀⠀⠀⠀⠈⠀⠀⣀⠀⠀⠀⣀
⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠢⠄⠁⠀⠀⠀⠀⠀⢀⡀⠠⠀⠒⠒⠲⠠⠁⠀⠀⠀⡁
⠀⠀⠀⡠⠲⠄⠠⡆⡀⠀⠀⠰⠂⠀⠀⠀⠰⠀⠁⠀⠀⠉⠁⠊⠀⠂⢻⡉⠉⠑⣀⠀⠀⡀⣀⠘⠀⠀⠤⠀⠀⠠⠀⠀⠈⠣
⠀⠀⠀⡀⠀⡀⠀⠀⠀⠀⠁⠀⠀⠐⠃⠀⠀⠀⠀⣀⠀⠰⠀⠀⠀⠀⠠⠀⠀⠀⠀⡄⠀⠀⠠⠀⠀⠀⢠⠀⠀⠀⠀⠀⠐⠃⠀⠀⠀⠀⠈⠀⠀⠀⠄
⠀⠀⠆⠀⠀⠀⠈⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠥⡀⠀⠠⠀⠀⠀⠰⠄⠀⠀⠀⠚⠀⠀⠀⡀
⠀⠀⠀⠁⠀⠐⠄⠤⡇⠀⠀⠰⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠛⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠐⠒⠀⡀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠊⢀⠀⠀⠁
⠀⠀⠀⠈⢄⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢏⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠉⠁⠊⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠾⠛⠀⠀⢀
⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢚⣐⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀


⠀⠠⠤⣄⣠⡀⢀⡀⢰⠄⡤⣀⣤⡀⣀⠀⠀⣀⡄⠀⠠⢀⢀⡀⣀⡤⢆⣤⢤⡴⢀⣦⣤⣥⣤⠒⣠⣶⣢⢦⡀⢀⠆⣀⣀⣁⣠⠂⠀⠠⠀⡀
⠀⠚⣿⡿⢋⡴⢋⣴⣿⣿⣿⣿⠇⢉⣴⣿⣿⣿⡿⣯⣾⢫⣎⣽⣿⣿⡿⠻⡟⡴⠟⢛⠟⠿⣭⣎⣿⣶⠿⣾⡷⢋⣾⡛⣟⡺⣽⣟⣿⢡⣾⡟⣸⣿⠤⠤⠄
⠀⢠⠍⠀⠃⠘⠋⢻⠁⠀⠄⠁⠁⠀⠉⠀⠈⠉⠁⠛⠀⠛⠛⠉⠀⠀⠀⠀⠀⠀⠠⠀⠈⡄⠇⠉⠉⠋⠀⠃⠀⠁⠙⠁⠀⠁⠁⠈⠃⠉⠙⢋⠁⠠⡀
⠀⠀⡀⠁⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⣀⠀⢥⠀⠀⠀⠀⡇⠀⠀⡀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⡶
⠀⠀⠁⠀⠀⠀⠀⡄⠀⠀⠀⠘⠀⡄⠀⠀⠀⠀⠀⡀⠀⠀⢀⡄⠀⠀⠁⠀⠘⠀⠀⠀⠀⢰⠀⠀⠿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⡇⠀⠀⠿
⠀⠀⠀⠀⠀⠀⠀⠁⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠨⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡦⠀⠀⠀⠀⠀⠊⠡⠈⠱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⡀⣀⠜⠀⠀⠀⠀⠀⠀⠀⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⡀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠰⠀⠀⠀⠀⠐⠂⠀⠐⠀⠀⠄⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣈⠀⢀⠀⠀⠠⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠀⣀⠄⠀⢠⠀⠀⡠⠀⠈⠀⠀⠀⠀⠁⠀⠁⠀⠀⠠⠀⠂⢀
⠀⠀⠀⠀⠀⠄⣈⣁⠠⠀⠐⠀⠫⠛⠀⠒⠂⠀⠀⠴⢀⠀⣁⠀⠀⢀⠀⠀⣀⠀⠀⠀⠀⢘⡃
⠀⠀⠀⠀⠤⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⡀⠂⠠⠀⠀⢁⠀⠀⡾⠀⠀⠈⠀⠀⠈⠀⢈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠐⢲⡄⠀⠀⢤⠄⠀⠐⠀⠁⠀⠀⠀⠄⠀⠂⠈⠀⠘⠀⠀⠁⠀⠀⠂⠀⢀⠀⠂
⠀⠀⠀⡀⠃⠀⠠⠀⠀⡀⠀⠠⠀⠀⠈⠀⢠⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠄⠀⠀⠐
⠀⠀⢠⣻⠀⠀⠀⠀⠀⠁⠀⠑⡂⠀⠁⠀⠘⠀⠀⠀⡆⠀⠉⠀⠀⠀⠀⠀⡀⠢⡀⠴
⠀⠀⠀⣀⠀⠀⠀⠀⠀⠄⠀⠉⠀⠀⡇⠀⠰⠀⠀⠀⠁⠵⠶⠐⢠⠘⠀⠀⠀⡀⢠⠀⠀⠐⠁⢀⡀
⠀⠀⠀⠀⠀⠁⠀⢃⠉⠁⠀⠈⠀⠌⢀⡀⠁⠀⠀⠐⠁⠀⠀⠀⠊⠀⠀⠰⢤⣀⠈⢁⡤⠞⠁
⠀⠀⠀⠀⠰⠆⠀⠂⠀⠐⠀⠘⠀⠀⠀⠀⠀⢀⠀⠀⢀⠄⠐⠈⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠠⠧⠀⠀⠀⠀⣀⠀⠀⠂⠀⠀⠚⢃⠀⠈⠓⠀⠠⡤⠒⠔⠀⠛⠒⠀⠋
⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠂⠀⣀⢀⡀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⢀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠀⠀⠀⠀⠀⠐⠂⠀⠒⠀⢀⠀⠀⢁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠐⠒⠛⠛⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠉⠡⠀⠀⠐⠀⠈
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣟⣙⣉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⣴⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡩⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤
⠀⠀⠀⠀⠀⠀⢒⣒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡶
⠀⠀⠀⠀⠀⣼⣟⣂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⣥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢒
⠀⠀⠀⠀⢐⣻⠵⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣛⣭⡿⠿⣟⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⡭⠗⠂
⠀⠀⠀⣠⣿⣓⣫⣭⠥⢤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⢛⣋⣛⣉⣍⣁⡀⠀⠀⠀⠀⠀⠀⠀⠠⠖⣊⣭⢄⣀
⠀⠀⠀⠴⠛⠉⠁⠀⠀⠀⠀⠉⠙⠒⠒⠂⠀⠀⠀⠀⠈⢋⡉⠉⠭⠤⠖⠚⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠂⠤⠤⠤



⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢑
⠀⠀⠀⠀⠀⠀⠀⠀⠲⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡿⡟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢄
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢤⠙⠂
⠀⠀⠀⠀⠀⠀⣨⣠⣶⣾⠿⠷⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢒⠶⠶⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡄
⠀⠀⠀⠀⠀⣘⣿⣿⣟⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠚⠒⠢⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠃⠀⠀⣠⠴⠂
⠀⠀⣀⣶⠶⠟⠋⠋⠉⠉⠉⠉⠁⠐⠒⠦⠤⠀⠀⠀⢠⠴⠞⠩⢭⣉⠈⠉⠓⠄⠀⠀⠀⠀⠀⠀⠀⢀⡁⠒⡈⠀⡀⢠⣀
⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠁⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠖⡀
⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠞⡇⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢜⠁⡀⠀⢀⣸⣆⣳
⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⢠⣶⡿⠀⠀⠀⠰⠀⠀⠀⠀⢏⡀⠀⠀⠀⠀⠠⡆⡂⠀⣿⡇⠀⢀⣼⣿⠏⣩⢷⡄
⠀⠀⠀⠀⠀⠀⢈⡇⡆⠀⠀⠀⠀⠀⢠⣭⡄⠀⠀⠀⠐⣆⡄⠀⠀⠼⠃⢈⣅⠀⠀⠀⢰⡏⣵⠀⠈⠠⠀⣁⣾⣿⠿⠁⠈⣉⠄
⠀⠀⠀⠀⠀⢀⣴⡏⠃⠀⠀⠀⠀⢠⠟⠛⠀⠀⣀⠀⢐⣍⣡⡄⢀⢸⠇⠈⠋⠠⡆⠀⣀⡗⢻⣀⠀⠁⢰⢹⣿⠁⣀⡤⠞⠻⣇⠀⣖
⠀⠀⠀⠔⢠⣿⣯⠦⠄⠀⠾⠂⠀⣤⣶⠀⠀⢠⣙⡂⢸⣇⣼⠃⢿⠀⠀⣰⣦⣀⡽⠚⠉⠉⠈⠉⢑⣦⡔⠈⣤⡾⡉⠀⠀⡀⠃⠀⠞⢆
⠀⠀⡌⢠⣿⠟⢏⡔⠒⢠⠋⠳⣀⠹⠍⣴⣤⠚⠿⠀⡾⠉⢹⡆⠀⠀⡿⢻⡇⣹⠛⠛⠛⠛⠛⠋⠉⣩⣤⡈⢇⢸⣥⠔⠊⠁⠀⡾⠃⠙⠧
⠀⠀⢳⡌⣷⢆⢹⡅⠢⠆⡌⠘⢘⠁⠀⠉⠉⠁⠀⠘⠁⠀⠀⢿⠄⠀⠁⠀⠀⢿⣿⢳⡖⢲⣶⣋⢾⣽⣿⠃⠀⠻⠃⡠⠎⠀⠀⡖⠀⠒⢳⡀
⠀⠀⠈⠣⣿⣿⣧⡜⠒⠢⢞⡳⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⢨⣧⠆⠀⠀⠀⠈⢿⣛⣛⣛⣛⣉⣈⣭⠇⠀⠀⠀⠙⠃⠀⠀⣴⠷⠒⠒⠚⢷⡄
⠀⠀⠀⠀⠈⠙⠋⠉⠁⠀⠈⠀⠀⠀⣤⣾⣿⣷⡶⠶⠀⠀⠀⢠⠇⠐⠤⠤⠔⠁⠀⠈⠛⠍⠭⠄⠚⠁⠀⠀⠀⠀⠀⠀⠐⠿⠿⠿⢿⣿⠿⠿⠿⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠿⠻⣇⠀⢧⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠈⣧⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⡆⡖⢀⠀⢀⡀⣀⠀⠀⠀⢀⠀⠀⣀⡀⢀⠀⠀⠄⡀⠀⡀⡀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠐⠡⠁⠇⠸⠁⠟⠀⢄⡃⠀⢈⠀⠐⠁⠐⠁⠈⠀⠇⠀⠏⠃⠃⠄⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢄⡀⠀⢀⣠⡤⠖⡀⠒⠁
⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⡀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠉⡡⠄⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠑⣦⡉⠀⠈⠀⠈⠁⢀⠐⢀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠘⠆⠀⠐⠦
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠷⠠⡤⠄⠉⠢⡀⠂⠀⠑⠀⡤⠀⠀⠲⡄⠀⠀⠀⠜⠀⢀⣀⡩
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⢠⠀⠀⠀⠀⠀⠀⠀⠀⣰⠀⠀⠀⠈⠀⢀⠳⠀⠀⠀⠈⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠦⡀⠀⠀⠀⡸⢿⠀⠀⠀⠀⢀⠋⢀⠀⣠⠄⠀⠙⠃⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⣠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣧⣜⢦⠀⠀⢰⡏⢀⣬⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠂⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠉⠀⠀⠀⠀⠉⠑⢦⡀⡘⢿⣦⣼⡷⠀⠀⠀⠀⠀⣀⠀⠀⡠⠀⢀⠀⠀⠀⠰⣇
⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡧⠀⠀⠀⠀⢠⡆⣠⣆⣻⣿⡈⣹⡋⠀⠀⠀⠀⠀⢀⠁⠀⠀⠀⠀⠘⢀⠀⠀⠀⠀⠐
⠀⢳⡀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠈⠀⠀⢀⠀⠀⢻⠿⠿⢋⠼⢿⡿⠟⠁⠀⠀⠀⠀⠀⠄⠀⠀⠀⢀⡠⠒⠉⠀⠀⡔
⠀⠀⠙⢦⣀⠀⢀⡇⠀⠀⡇⠀⠀⠀⠀⠴⣿⠀⠀⣾⣶⣿⡃⢠⣿⡇⠀⠀⠀⠀⠀⢀⡌⠀⣀⡠⠖⠚⠁⠀⠀⠀⠀⢠⠀⢀⡤
⠀⠀⠀⠀⢉⡑⡄⣳⡄⢀⠀⡀⠀⠀⠀⠀⠈⢆⠀⣈⠉⠹⣿⠿⣿⡇⠀⠀⠀⢀⣔⣡⣦⣤⡅⣠⡀⠆⠀⠀⣠⣴⡟⢲⢆⠞
⠠⡄⠀⠀⡌⢳⣴⠿⠛⠃⠀⢱⠀⠀⠀⠀⠀⠀⡞⠁⠀⠀⠀⠀⣿⡇⢀⣤⠶⠟⠋⠉⠉⠉⣉⠀⣠⣼⣶⣾⣿⢿⠔⢀⠊
⠀⠀⠀⠀⠸⡈⢿⠀⠂⠀⠀⠀⡄⠀⢀⠔⠀⠀⠁⢠⡀⣦⡀⠀⠿⡷⠿⠤⣀⠀⠀⠾⠇⠀⢛⠛⠛⠁⣿⣿⡷⠀⠀⣸⠦⣤⠄
⠀⠀⠀⢠⠀⠰⠀⢦⢆⠀⠀⠀⡄⢀⠀⣠⣿⣄⡁⠺⣿⡿⠟⣦⣴⣿⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠈⢿⡟⠥⠀⢀⠟
⠀⠀⠀⠀⠁⢠⡰⢼⣿⣦⠀⠀⠀⣀⣰⡿⠛⠁⠀⠀⣀⠀⣲⣽⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈⢳⣶⣶⠁
⠀⠀⠀⠀⠀⠀⠉⠚⢿⡿⣷⣄⠃⢻⡟⢀⢀⡀⠀⠀⠻⢿⡿⢟⡈⢈⣦⠀⠀⠀⠀⠀⠀⠀⠄⠠⠀⠀⠀⠀⠙⢿⡋⠁
⠀⠀⠀⠂⠀⠀⠀⠀⢠⣷⠶⠋⠁⠀⠈⢠⡁⠀⠀⠀⠀⠀⠀⢛⣿⣾⠟⠀⠀⠀⣠⡆⠀⠀⠈⠀⠐⢆⡀⠀⠀⠁⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠃⠀⠀⢿⡿⠃⠀⠀⠀⠀⠠⠀⠙⢦⣄⠀⠀⠀⠀⡾⠁⠀⠀⠀⠀⠀⠈⠁⢲⣶⣤⡀⠀⠀⠙⣀⠀⠀⠠⢴⠒⠋⠀⠀⠀⠀⣀
⠀⠀⠀⠈⠀⠀⢸⡟⢠⠤⠀⠀⠀⠀⠀⠀⠀⠀⠙⢆⠀⠔⣰⠂⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢿⠻⣄⣀⣀⡈⢋⠀⠐⠁⠀⠀⠀⡠⠐⠁
⠠⠴⠆⠀⢀⣺⠏⢀⠀⠀⠀⠀⢀⠀⡄⠀⠀⠀⠀⠈⠆⣼⠃⠀⣠⠐⣦⣠⡀⣴⡄⢠⡟⠁⡄⠀⠿⠋⢉⣠⠘⠛⠁⠀⢠⠂⠊
⠀⠀⠀⠀⢬⠏⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠻⢿⣿⠙⠿⢿⡷⠋⠀⠊⠀⠴⠒⠉⣠⡀⠀⢀⠠⠀⠲⠲⠶
⠀⠀⠀⢠⡆⠀⠒⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠼⢀⣠⡶⠾⠛⢫⡁⠉⠙⠺⣄⠉⠀⠀⠀⢀⠤⠤⠿⢄⣃⡀
⠀⠀⠀⣨⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣶⠄⠾⠏⢁⡘⢠⡄⣴⢉⣷⡄⠀⠀⠱⠆⠀⠈⠀⢀⣠
⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠀⠂⠀⠻⢿⡿⠇⠙⠿⠛⠀⠀⠀⠀⢀⠀⠙⠻⢯⣴⣄⡀
⠀⠀⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠙⡟⠛⠹⢲⠴⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⢀⠈⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⠑⠀⠀⠈⠀⢠⣶⣼⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢸⣿⠟⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠙⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠟⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⣠⣾⠀⢐⡆⠀⣷⣌⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠉⠀⡌⠳⡀⠉⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢏⡉⠀⠀⠈⡹⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠠⢶⠆⢀⢁⣀⣠⡀⠄⠐⡶⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠌⠁⢹⡇⠘⠰⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⣿⢿⢹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⣼⠃⠘⣧⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣫⠞⠁⠀⠀⠈⠳⣝⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⣶⣩⣤⡅⡀⢀⡄⢠⡀⣀⢨⣤⣉⣲⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢏⣀⠜⣠⢞⣴⠃⡼⠃⠘⣧⠸⣆⠳⡄⢏⣀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⢞⣥⠞⠡⠚⠁⠀⠀⠈⠓⠌⠳⣌⡳⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣚⣉⣒⣉⠤⢶⢆⠀⢠⠀⢠⡄⠀⡴⡶⠤⣉⣂⣉⣒⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠈⡁⠀⢀⡴⣣⡿⢀⣿⠀⠸⣧⠀⢻⣜⢆⠀⠀⢙⠁⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⢀⡴⣋⣴⠟⣠⡾⠃⠀⠀⠙⢷⡀⠻⣧⣕⢦⡈⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⣒⣥⠾⠋⣡⠶⠋⠀⠀⠀⠀⠀⠀⠙⠦⣀⠙⠳⣭⣒⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢯⣄⡈⠥⢤⣄⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢠⡤⠤⣉⡀⣽⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡁⢀⠅⢀⡤⢊⡾⠀⢀⡾⠀⢠⡟⠀⠘⣧⠀⠸⣆⠀⠸⣆⠑⢆⡀⠐⡃⠀⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣁⠴⣋⣴⠟⠁⣰⠟⠁⣠⠟⠁⠀⠀⠙⢧⡀⠙⢷⡀⠙⢷⣄⡙⠦⣈⠁
⠀⠀⠀⠀⠀⠀⠀⣀⡤⢖⣋⣵⠾⠛⣁⡴⠞⢁⣠⠞⠁⠀⠀⠀⠀⠀⠀⠙⢦⣀⠙⠷⣄⡙⠻⢶⣬⣙⠲⢤⣀
⠀⠀⠀⠀⠀⢾⣉⠁⠈⠉⠁⢀⣀⣈⡁⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⢉⣀⣀⡀⠉⠉⠀⠈⣉⡷
⠀⠀⠀⠀⠀⢰⠉⢻⠉⠉⠉⠁⡠⢎⡅⠀⢠⠀⠀⠀⣴⠀⢰⡆⢰⡀⠀⡄⠀⠀⢠⡀⠀⣦⠱⢄⠈⠉⠉⢉⡟⠉⢀
⠀⠀⠀⠀⠀⠘⠂⠊⠀⣀⠴⢋⣴⡿⠁⣠⡟⠀⢀⣼⠇⢀⣿⠁⠸⣧⡀⢻⣆⠀⠈⢷⡀⠘⣷⣄⠙⢦⣀⠀⠓⠐
⠀⠀⠀⠀⠀⢀⣠⠴⠚⣡⣴⡿⠋⣠⣾⠏⠀⣠⡾⠋⣠⡿⠁⠀⠀⠙⢷⡄⠹⣧⡀⠈⠻⣦⡈⠻⣷⣤⡈⠑⠦⣄⡀
⣀⣠⡤⠖⣚⣩⣤⣶⠿⠛⢉⣠⡾⠛⢁⣠⠾⠋⣠⡾⠋⠀⠀⠀⠀⠀⠀⠙⢦⣌⠛⢦⣀⠈⠻⣦⣀⠙⠻⠷⣦⣤⣉⣓⠲⢤⣄
⠙⢤⣀⡀⠉⠁⠀⠀⠀⠒⠋⠁⠀⠒⠋⠁⠀⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠈⠓⠂⠀⠉⠛⠒⠀⠀⠀⠉⠁⢀⣀⣤
⠠⡋⠀⡉⠉⠉⠁⠒⠒⠒⠒⠒⠒⠒⠊⠉⠉⠉⠓⠒⠖⢒⠒⠒⠒⠒⠒⠖⠒⠊⠉⠉⠉⠑⠒⠒⠒⠒⠒⠒⠒⠉⠉⠉⢹⠃
⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢸⢰⡇⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢸⠀⠇⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢀⡀⠀⡰⠃⠀⠀⠀⠀⠀⠀⠣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠚⠉⠀⠀⠀⠀⠀⠀⠀⠉⠀⠒⠂⠠⠤⠤⠀⠒⠛⠂⠀⠉⠉⠉⠁⠀⠒⠢⢤⣀

⠀⢀⡀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀
⠀⠈⠁⠀⣀⣄⠀⠀⠐⣾⣷⠂⠀⢀⣀⠀⠀⠛⠛⠀⠀⠀⠀⠀⠐⣮⣷⣿⡄⠀⠀⠠⡄⠀⠀⠀⠀⠀⠀⠘⠟⠀⠀⠰⣾⡶⠀⠀⠀⠿⠆
⠀⠀⠀⠀⠻⠟⠀⠀⠀⣹⣏⡀⠀⠀⠁⢀⣀⠀⠀⠀⢿⡷⠀⠀⠈⠽⢻⡛⠂⠀⠀⣸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣽⣍
⠀⠠⣴⣶⣆⠀⠀⢠⣼⣿⣿⣧⡄⠀⠀⠻⠿⠃⠀⠀⣼⣇⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⡆⠀⠀⠀⣾⣿⠀⠀⠀⠈⢻⣿⣿⠁⠀⠀⢠⡄
⠀⠈⠿⢿⠓⠀⠀⠶⣿⣿⣻⣿⠶⠀⠀⠀⠀⠀⢀⣼⣿⣿⣦⡀⠀⠠⡤⠀⢀⣰⣾⢿⣿⣷⣦⡀⠀⠀⢀⡀⠀⠀⠻⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⢶⣾⣿⣿⣿⣿⣷⡶⠀⠀⠀⠀⢠⣿⣿⣿⣿⣄⠀⠀⠀⠀⠈⣹⣿⣿⣿⣿⣟⡁⠀⠀⠛⠃⠀⢲⣾⣿⣿⣿⣿⣶⠂
⠀⠀⠀⠀⠀⠀⠉⢽⡿⣟⣿⣿⡯⠉⠀⠀⠀⠀⣴⣿⣿⣿⣿⣦⠀⠀⠀⠀⢾⣿⣟⢛⣿⣟⣿⣷⠆⠀⠀⠀⢤⣴⣿⣿⣿⣿⣿⣷⣤⠄
⠀⠀⠿⠆⠀⠀⢻⣿⣿⣿⣿⣿⣿⡖⠂⠀⠀⢠⣾⣿⣿⣿⣿⣷⡄⠀⠀⠀⣤⣿⣿⣿⣿⣿⣿⣥⠀⠀⠀⣀⣤⣿⣿⣿⣿⣿⣿⣿⣇⡀
⠀⠀⠀⠀⢀⣠⣴⣿⣶⣻⣿⣿⣿⣧⣄⡀⠀⠰⠿⠿⠿⠿⠿⠿⠦⠀⢀⣿⣿⣿⣿⣷⣿⣿⣽⣿⣿⡆⠀⠉⠻⠿⠿⠿⡿⠿⠿⠿⠿⠟⠁
⠀⠀⠀⠀⠈⢽⣿⣿⣿⣿⣿⣿⣿⣷⡿⠁⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠈⣉⣻⣿⣿⣿⣟⣿⣿⣿⣉⠁⠀⢠⣤⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠘⢻⣿⣽⣟⣿⣿⣿⣟⣿⣴⣿⣿⣿⡟⠃⠀⠀⢀⣄⠀⠈⠁⢀⣶⣿⣿⡋⣻⣿⣿⡿⣿⣿⣿⣶⡀⠀⠉⠀⢀⠀⠀⠀⠀⣿⣿⣧⠂
⠀⠀⠀⠈⠹⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠉⠀⠀⠀⠘⡟⠀⠀⠀⠈⢛⣿⣿⣿⣿⣿⣿⣤⣼⣿⣿⡛⠃⠀⠀⠠⣿⡿⠄⠀⠀⠘⠙⠋
⠀⠲⢶⣿⣿⣿⣿⣷⣯⣿⣿⣿⡿⢿⣿⣿⣿⣶⠖⠀⣰⣧⠀⠀⠀⣸⣿⣿⢻⣿⣿⣟⣿⣿⣿⣿⡿⣿⣷⡀⠀⠀⣸⣇
⠀⠀⠐⠛⠻⠿⠻⠿⢿⠿⠟⠿⠻⡟⠿⠟⠛⠂⠀⠿⣿⣾⠿⠂⠈⠻⠛⠿⠻⠿⠻⠿⠿⠿⠿⠟⠻⠟⠛⠃⠀⣨⣿⣿⣄⠀⠀⠀⢠⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⣤⣤⠛⣿⢦⣤⠄⠀⠀⢠⣤⡀⠀⠀⢠⣦⠀⠀⠀⠀⠀⠀⢀⢿⣿⣿⣿⡀⠀⠀⠘⠛⠁
⠀⠀⠀⠀⠀⣶⣷⡀⠀⠀⢠⣠⡄⠀⠈⠁⠀⠀⠙⢻⣿⣿⣿⠛⠀⠀⠀⠘⠟⠃⠀⠀⢨⣯⠀⠀⣴⡦⠀⢠⣿⣿⣽⣿⣽⣿⡄⠀⣶⡄
⠀⢀⣄⠀⠀⢈⣍⠀⠀⠀⣿⣿⣿⠅⠀⠀⢸⣷⢶⣿⣿⣽⣿⣳⣶⡇⠀⠀⢀⡀⠀⠰⣿⣿⣷⠀⠀⠀⠀⢀⣹⣿⣿⣿⣿⣯⠀⠀⠈
⠀⠀⠁⠀⢀⣿⣿⡃⠀⠀⠀⠉⠉⠀⠀⣠⣀⢙⣻⣿⣿⡟⢻⣟⣛⣁⣤⠀⠈⠁⠀⣸⣿⣿⣿⡀⠀⠀⠀⠘⣿⣿⣿⣿⣿⢿⠃
⠀⠀⠀⠀⣼⣿⣿⣿⠀⠀⠀⢾⡷⠀⠀⢻⣿⣿⣿⣉⣿⣿⣿⣿⣯⣿⡿⠀⠀⠀⢀⣿⣿⣿⣿⣇⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣷⠀⠀⢀⡀
⠀⠀⢀⣾⣿⣿⣿⣿⣿⡆⠀⠀⠀⢠⣄⣀⣉⣽⣿⣿⣿⣻⣿⢿⣿⣍⣀⣀⣄⠀⣸⣿⣿⣿⣿⣿⡄⠀⣀⣟⣿⣿⣿⣿⣿⣿⢿⣀⠀⠈⠁
⠀⠀⠈⣹⣿⣿⣿⣿⣿⡁⠀⠀⠀⢸⣿⣯⣿⣿⢿⣿⣿⣿⣿⣴⣿⣿⣿⣿⡟⠀⠉⠉⠉⠉⠉⠉⠉⢴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⣰⣿⣿⣿⣿⣿⣿⣧⠀⠀⣄⡀⠙⢛⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣛⠋⠀⣠⡄⠀⢰⣶⡆⠀⢠⣶⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⡄
⠀⢴⣿⣿⣿⣿⣿⣿⣿⣿⡦⠀⢿⣿⣿⠛⢻⣿⡿⣿⣿⠿⣿⣿⣧⣠⣿⡿⣿⣿⠃⠀⠈⠉⠀⢀⣿⣿⣿⣾⣿⢿⣿⣿⣿⢿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠷⠿⠿⠿⠿⠿⠶⠿⠿⠿⠿⠿⠟⠛⠁⠀⠀⠀⠀⠀⠛⠛⠻⠿⠻⠿⠿⠿⠿⠿⠿⠟⠿⠟⠛⠛
⣶⣶⣶⣶⣶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡖⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣉⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠶⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣽⣿⣿⢯⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⢀⡘⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣧⣴⣿⣄⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠟⠀⠈⠀⠘⠋⠈⢻⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣰⣏⣈⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠏⠰⠷⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣯⣀⣽⣧⡀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡿⠃⠰⠀⠀⠀⠀⠸⠿⠂⠙⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢼⣿⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣚⣿⡒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣽⣭⢯⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣘⣵⠟⣯⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣅⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣘⣿⣨⣿⡤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣶⠎⢣⠆
⠀⠀⠀⠀⠀⠀⠀⢠⡀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⣹⣿⣷⣾⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⣴⣶⣻⡤
⠀⠀⠀⠀⠀⠀⢀⣆⡁⠔⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣷⣿⣿⣿⣿⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⡝⢖⣠⠙⠧⠦
⠀⠀⠀⠀⠀⠀⢰⣅⣈⠉⢁⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣴⣿⠟⣃⣽⣷⣾⠥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠿⢾⡆⠀⠛⢾⣛
⠀⠀⠀⠀⠀⡘⠓⠆⠀⠘⠁⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣿⣿⣾⢻⣿⠻⣷⡶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⢫⡵⢺⣄⢶⠬⠆
⠀⠀⠀⠀⡀⠛⠀⠒⠒⠀⠂⢉⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⣽⣿⣷⣾⣿⣿⣿⠃⣤⠀⠀⠀⠀⠀⠀⠀⠀⠈⢋⣓⢛⣃⣈⠡⠀⢩⠺⠋
⠀⠀⠀⢠⡈⠹⠲⠐⠢⠈⠋⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣏⣸⣿⣿⣿⣿⣿⣿⣆⢀⠀⠀⠀⠀⠀⠀⠀⠙⢰⡋⣨⠉⣐⠒⠳⠟⠒⣪
⠀⠀⠀⠸⠧⠲⠀⠲⠒⠲⠀⠀⠪⠁⡀⠀⠀⠀⠀⠀⠀⢤⣤⢼⣽⠟⡡⢾⢋⣯⢸⣿⣛⣁⣠⠀⠀⠀⠀⠀⢈⣔⣩⠿⣿⠞⣽⣆⠑⠎⢛⡤⣠⡤
⠀⠀⠰⡄⠁⠄⣤⠀⠀⠒⠀⠐⠂⠁⠀⠄⠀⠀⠀⠀⣀⠀⠙⣛⣿⣾⣿⣿⣼⣿⣿⣿⣿⠏⠁⠀⠀⠀⠀⣀⠲⠌⡥⢨⣍⣠⡅⠀⠴⢓⣠⣆⢁⣠
⠀⠐⠦⠈⠁⠀⠈⠈⠁⠀⢡⡀⠀⠂⠁⠰⡀⠀⠀⠀⠙⠦⡷⢟⣵⣞⣡⣼⣿⣿⣿⣿⠿⣶⣇⡶⠃⠀⠀⣭⣿⡾⣤⣬⠁⠈⡛⠁⠀⠋⠹⠯
⠀⠘⠠⢘⢉⣉⡀⠙⣀⠀⡀⢀⠀⡀⠀⠀⠉⠀⠀⠠⢴⣦⣾⣿⣿⠟⢿⣿⣿⣦⡜⡿⠓⢫⣝⢢⡀⠀⠰⠮⣴⡖⣠⢲⣆⣿⡇⠨⠛⢷⠄⣿⠛⠤⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢾⣿⠶⠻⢿⣜⢻⣿⣾⡿⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠉⠁⠀⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠶⠚⠛⠉⠉⠉⠛⠛⠒⠒⠶⠦⢤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⣀⡴⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠓⠶⣤⣦⡀
⠀⠀⠀⠀⠀⣤⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠁⠀⠙⣦⡀
⠀⠀⠀⠀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⠁⠀⠀⠀⠠⠬⠷⣄
⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠒⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧
⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷
⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠴⠞⠻⢷⣶⣶⣾⠂
⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⣠⠤⠞⠁⠀⠀⠀⠀⠀⠀⢀⣠⡴⠞⠋⠉⠀⠀⠀⠀⠀⠈⣼⡟
⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⣿⠔⠊⠉⠀⠀⠀⠀⠀⠀⠀⣠⡴⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⡀
⢀⣴⠶⠋⠀⠀⠀⠀⠲⠀⢰⣿⡄⠀⠀⠀⠀⠀⠀⢀⣴⠟⠉⠀⣠⠞⠉⠙⢦⣠⠞⠉⠑⢦⡀⠀⣀⣀⣤⣽⣷
⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⠠⠀⠀⠀⠀⣠⠟⠁⠀⠀⡼⠁⢠⣶⣤⠈⠁⠀⣤⣶⡄⢳⡀⠘⠻⠿⢿⣥⡀
⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡟⢶⡇⠀⠀⣴⠏⠀⠀⠀⢸⠇⠀⠈⠛⠁⠀⠀⠀⠈⠋⠀⠀⢷⠀⠀⠀⠀⠙⢿⣦
⠈⢻⡀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠃⠀⠻⢦⣴⣿⣶⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠈⠻⣦
⠀⠘⢧⣀⠀⠀⠀⣀⡴⠛⠉⠀⣾⣿⠿⠾⠟⠛⠁⠀⠀⠀⠈⢧⡀⠀⠀⠀⣠⢦⡀⠀⠀⠀⢠⠟⠀⠀⠀⠀⠻⢿⣿⣿
⠀⠀⠀⠉⠙⠛⠋⠉⠀⠀⠀⢀⣈⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⠶⠚⠁⠀⠙⠲⠶⠚⠋⠀⠀⠀⠀⠀⠀⠀⠉⠻⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣿⡿⢿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠟⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣤⡿⠃
⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣶⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠛⠟⣻⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣦⣄
⠀⠀⠀⠀⢿⣿⣛⡉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠈⠓⠞⠁⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣶⣄⡀
⠀⣠⣤⣤⣴⣾⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⢫⡧⢤⠄⠀⠀⠀⠀⠀⠀⠀⣤⢬⣏⠲⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣿⣿⡆
⠀⠘⠿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⢧⡀⠀⠀⠀⠀⠀⠀⠀⡨⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣽⡿⠃
⠀⠀⠀⠈⣹⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠙⡄⠀⠀⠀⠀⠀⡞⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣇
⠀⢠⣶⠿⠋⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⢠⠶⣸⠉⠙⠒⠃⠀⠀⠀⠀⠀⠓⠊⠉⣇⡴⡆⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⣄
⠀⠙⢿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⠋⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠘⠶⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣻⣿⣿
⠀⢠⣿⣋⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⠋⠉
⠀⠈⠛⠛⠛⠛⠛⠛⠛⣿⣷⠆⢀⣠⣤⣤⣶⠶⠶⠶⣶⣤⣀⣀⣀⡀⠀⢀⡀⠀⢀⣤⣶⣶⣦⣄⠀⠀⢀⣀⣀⣠⣤⣦⣤⣶⣶⣶⣶⣶⣶⡶⢾⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⡿⠿⠛⠋⠉⠛⠁⠀⠀⣀⣽⠉⠉⠉⠙⠿⣦⣿⡿⣿⠿⠃⠀⠀⠈⠻⣷⣶⡟⠋⠙⠛⠃⠀⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠁⠀⠀⠀⠀⠀⠀⠈⢹⡇⣿⠀⠀⠀⠀⠀⠀⠈⠀⠙⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠛⠛⠓⠒⠒⠚⠃⠛⠒⠒⠒⠛⠛⠛⠛⠛⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⢀⠀⢀⣠⡀⠀⣠⣤⠤⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⣾⣿⣿⣿⣤⣶⣾⣽⣿⣶⣾⠅⣂⡠⠼⠤⠤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠖⠟⠉⢶⣿⣷⣿⣟⣿⡿⢿⣯⣿⣿⣥⡟⢺⡤⣗⠒⠒⠐⠂⠛⣤
⠀⠀⠀⠀⠀⠀⠀⢰⢃⣜⣢⣼⡿⣯⢿⣿⣏⣹⣇⣿⡿⣟⢯⠻⣿⣿⣤⣿⣷⣶⣀⣤⣞⢿⣷⡂
⠀⠀⠀⠀⠀⠀⠀⠸⣯⣼⣿⣿⣿⣿⣿⡿⠿⠉⠙⣿⣿⣜⡎⢃⠣⢸⣻⣿⢿⣽⣿⣷⣼⠘⡏⣷⡄
⠀⠀⠀⠀⠀⣴⣦⣜⣿⣿⣿⣿⣿⢛⣂⣇⠀⢀⠼⠛⢿⣿⣿⠛⠒⠓⢿⣿⣿⣿⣿⣻⣿⣧⣇⣲⣿
⠀⠀⠀⠀⠀⡯⣷⢻⢷⣿⣿⣿⡟⡛⠉⢙⠖⠉⠀⢀⠔⠉⢳⣄⠀⠀⠀⣿⣿⠏⣸⣿⣿⣿⣿⣿⣿⣦⡄
⠀⠀⠀⠀⠀⡗⣿⢼⢊⣿⣅⣝⢳⠄⠀⣠⠃⠀⠀⠸⠀⠀⢸⡿⠀⠀⠀⢿⡿⣾⣏⣿⣿⣯⣿⣿⣿⣿⠷
⠀⠀⠀⠀⣰⠖⠛⢾⣸⣿⣿⣯⣨⣶⣾⣯⠀⠀⣠⡃⠀⠀⠘⣇⢣⡀⠀⠀⠛⠻⣽⣷⢻⣯⣅⡼⣌⠙⡄
⠀⠀⠀⠀⣽⢂⠀⠀⠈⢯⣿⣿⣿⣽⡟⠁⠀⢰⣯⣤⣤⠄⣭⣿⣯⡵⠀⠀⠀⢰⡟⠃⠁⢺⡤⢶⠃⠀⠨⡂
⠀⠀⠀⠀⠘⡄⢰⡀⡀⠸⣷⣿⣿⡿⢟⣧⡀⠀⠀⠀⠈⠒⠋⠀⠀⠀⠀⣀⣤⣾⣟⠀⢀⣉⣷⣤⣁⠀⢀⠇
⠀⠀⠀⠀⣤⠛⠋⠉⠃⣢⣼⣿⣿⣏⡙⠲⢷⡄⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣽⣿⣿⢿⣿⣿⣽⡏⠃
⠀⠀⠀⠀⠘⢶⡂⢀⣀⠯⣨⣿⣹⣿⣿⣏⣺⣿⣻⣷⣦⣀⠀⢀⣤⣺⣿⣟⢙⣿⡿⣿⣿⡿⣿⣿⣾⠇
⠀⠀⠀⠀⠀⠀⠈⠱⣿⣾⣿⣿⣷⣿⢿⣿⣽⣁⣽⣿⣿⣿⣭⣵⣶⣾⣿⣿⣾⣯⣿⣿⣛⠄⢻⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⡟⠋⠉⠙⢿⣽⣻⣿⣿⣿⣿⡟⣠⠿⣿⣾⣿⣿⣿⣿⣿⡆⠀⢀⡼⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣆⠀⣄⣘⢼⣹⣍⣿⣿⣿⣿⣿⣿⡽⡋⣟⣺⣿⣾⣽⡗⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠿⢿⣿⣿⣿⣝⡻⢭⣩⠿⠬⠤⣥⡽⢻⠿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠓⠛⠉⠹⡿⠿⠛⠁

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡜⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢓⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠹⢿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣬⣿⣶⣷⣧⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⢟⣯⢠⡙⣓⢿⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣿⣷⣤⣭⡿⢨⣭⡷⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣨⣍⠉⣉⣉⣤⡺⠿⠏⠳⣟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡿⣿⣿⣿⣿⣟⡻⢿⠛⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣾⣿⣭⣤⣤⣨⣭⣀⠛⣿⣿⣶⣦⣌⣥⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣏⠻⡟⠿⠿⠿⠿⠿⠿⠿⢛⡿⠟⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣤⣿⣶⢎⣼⣷⣬⠑⠚⢷⣾⣿⣿⣛⣿⡧⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣨⣿⠿⣥⣿⣯⠗⣴⣾⣿⣷⣦⣶⠒⣼⣶⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣦⡺⠚⠻⠿⠯⠿⠿⠈⠿⠿⠟⠿⣀⠾⠟⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠶⠍⠻⠷⣾⣷⡶⠖⢂⡴⣶⣶⣖⣢⣶⣾⣿⣿⣷⣶⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠉⣉⣁⡐⣱⣶⣿⣿⣤⣿⣿⣿⣿⣯⣼⣿⡀⣈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠮⠽⠏⢿⣮⣍⣭⣭⢹⡅⣠⠴⣦⣍⣭⣿⠷⠿⠿⠟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⠀⢽⡷⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢶⡄⠘⣷⣿⣿⣦⣁⣠⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢷⣏⣿⣿⣿⣟⣯⠤⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢶⣈⣺⣿⣿⣿⣿⡹⠷⢦⣶⡦⢤⡶⠶⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣐⠿⣿⠋⠉⢻⣟⣿⣀⠀⠄⠀⠀⢠⣾⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠉⠹⣾⣷⣤⠔⣹⣿⠿⡉⢙⣵⣶⡦⠀⣡⡴⠶⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣶⣶⣰⣿⣃⡩⢽⣻⣯⣿⣙⣌⣥⣷⣿⣷⣶⣾⣿⣋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⠄⠉⠤⠆⢈⣿⡿⣿⡿⠿⢿⣿⣿⣍⢉⡈⠭⠉⠁⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⢀⣴⣦⣈⡋⢿⢿⣇⠀⠀⣹⣷⣦⣤⣤⣤⣤⣶⠛⠛⢉
⠀⠀⠀⠀⠀⠀⠀⢀⡘⠓⠀⠀⣀⣛⠻⠟⠿⣻⣿⣾⣝⣓⠺⢛⣛⣵⣿⣿⣾⡵⠀⠀⠀⢠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣱⣤⣼⣿⡀⠀⢸⣏⣿⣿⣿⣿⣿⣿⣯⠃⠙⢻⠁⣤⣶⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠈⠉⢛⠻⠟⣻⣿⣮⣿⣿⣿⡿⣾⣿⣿⣻⡵⠾⠿⡿⠟⢿⠿⠷
⠀⠀⠀⠀⠀⠀⠐⠾⡿⣶⣾⣧⣿⣶⣶⡿⡟⢿⣿⠂⣟⣧⣿⣿⣿⣟⠀⠀⢀⢼⣦⠶⡀
⠀⠀⠀⠀⢀⠀⠀⠀⣤⣄⣴⡄⡡⣈⡲⣤⣤⣾⣟⣯⣿⣿⣹⣿⣿⣿⣶⣀⣩⣿⣷⣶⣯⣭⣀
⠀⠀⠀⠀⠹⢿⣷⣶⣤⣉⣉⠙⢡⣝⣛⣚⣷⣿⣿⠿⣅⡻⡻⡿⢿⣷⣉⣿⣿⡷⣦⣤⣭⣍⠙⠓
⠀⠀⠀⠀⠀⠃⠀⢉⡙⡙⠛⢻⣿⣿⣿⠟⠙⠙⢿⣿⣿⣿⣿⡿⣄⣛⣽⣿⣿⣯⠚⡇⢉⣉⣀⡀
⠀⠀⠀⠀⠀⣀⣀⣤⢤⠶⠞⠋⢉⣿⣿⠀⣀⡀⢩⣿⣿⣿⣿⣿⣍⣭⣟⠁⠀⠨⣿⣿⣿⣶⣤⣤⣤⡄
⠀⠀⠀⠀⠚⠋⠉⠀⠁⠀⣠⣴⣿⢫⣷⣶⣶⣾⠿⣿⣿⣿⢻⣟⢻⣧⣿⣾⣭⠾⣿⢯⡀⠈⠙⠛⠋⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿⠛⠛⠙⠛⣻⡿⡿⠋⢀⣿⠃⣿⡈⢿⣦⡈⠱⢶⣅⠀⠈⠃⠀⠁
⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠴⠟⠉⠀⠀⠀⠘⠁⠀⠸⣿⡀⠉⠇⠀⠀⠉⠷⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠇⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⣼⣿⢋⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣈⣽⠟⢫⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣽⣿⣿⣷⣿⣶⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣦⠘⢿⣿⡿⠿⠿⣯⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⣽⣿⡿⠛⣧⡀⣀⡿⠷⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣬⠁⠉⢹⣶⢿⣿⠿⣧⣴⡖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⢿⣷⣶⣿⣷⣼⣿⣦⣾⣿⣶⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣶⣴⡟⠉⠉⣻⡏⢹⣿⠀⠀⢻⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠶⠘⢾⣿⣦⣴⣿⣿⣿⣿⣷⣴⣿⡾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡀⠀⢰⣿⣋⣿⡏⠀⠀⢹⣿⡉⢉⡿⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⡿⣿⣿⣿⣶⣶⣿⠻⣿⣿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣆⢀⣿⣿⠀⠀⢘⣿⡋⠈⣻⣿⡿⠿⣿⣦⣴⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠭⣿⣿⣿⣿⣷⣶⣾⣿⣿⣿⣿⣿⠀⠀⣹⣿⣥⣽⣟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣏⠁⢹⣿⣿⣅⣿⡿⠛⢻⣿⣿⠟⠉⠉⣿⣦⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣶⣶⣿⣿⡷⣿⣿⠟⠻⢿⣿⣦⣾⣿⣿⣶⣀⣴⣿⣷⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣛⣻⣧⣄⣽⣿⣤⣿⣇⠀⠀⣸⣿⣿⣧⣀⣿⡿⢻⣿⣿⠁⢉⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡸⡿⠛⢿⣿⠿⠿⢿⣿⣿⣿⣾⣿⡿⢿⣿⣿⢿⣷⣾⣿⢿⣿⣿⣟⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣽⣿⣦⣤⣾⣏⠀⠀⣸⣿⡃⢉⣿⣿⣷⣾⡿⠁⠀⢨⣿⣤⣀⣸⣮⣉⣉⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⢻⣿⣿⣿⣿⣿⣿⠟⢙⣿⣿⣿⣁⢈⣿⣿⣶⣴⣾⣿⣿⣿⣿⣿⣿⣿⣏⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣉⣼⣿⣿⠿⢿⣿⣿⠟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⡿⠿⠿⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡵⠋⠉⠀⠈⠁⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢸⢸⠀⠀⠀⠐⠂⠀⠶⣤⠀⠀⠀⠀⠀⠀⠀⠀⢀⣇⠀⠀⠢⠀⠀⢠⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢸⢸⠀⠀⠀⠀⠀⠀⠀⠉⠀⠦⠀⠶⢤⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠉⠀⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢃⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎

⠀⠀⠀⡤⢀⠤⡀⠀⠀⠀⠀⠀⠀⠀⢠⢄⡠⡄⠀⠀⣠⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⠀⠀⢀⡀
⠀⠀⠀⣡⢿⡈⠀⠀⠀⠀⠀⢀⡀⠀⠀⢸⠃⠀⠀⠀⢩⠄⡠⠹⠄⠀⠀⠀⠀⠀⠨⠥⠀⠠⠬⠀⠀⠈⠁
⠀⠀⠀⠉⣺⠈⠒⠀⠀⠀⣠⣾⣿⡀⠀⠠⠂⡁⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠉⢸⠿⣿⣿⠿⡄⠉
⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠁⠀⠀⠀⠀⠁⠂⠁⠀⡤⠀⠀⠀⢠⠄⠀⣼⡇⠀⠀⠀⠀⢸⠇⠀⠀⠀⣲⣆
⠀⠀⠀⠀⢰⣄⠀⠀⠀⠀⣀⣀⣀⠀⠀⣴⣶⠀⠀⣤⣤⣤⣤⣤⡄⢀⣿⣿⠀⠀⠀⠀⠸⠂⣠⣤⣤⣌⠁
⠀⠀⠀⣴⣿⣿⣧⠀⠀⠀⠈⠉⡧⠀⠀⠈⠀⠀⠀⠻⢿⣿⣿⣿⠀⣸⣿⣿⡇⠐⣞⣳⠂⠘⠋⣉⢉⠙⢧
⠀⠀⠈⣉⡤⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠈⠉⠉⠀⠀⠉⠉⠀⠀⠙⣀⠂
⠀⠀⠀⠈⠠⠈⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠒⠀⠒⠀⠀⠀⣠⡀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠸⡿⠀⠀⠀⠀⢿⠿⠆⠀⠀⢠⣶⣶⡄⠀⠀⠀⠀⠴⠿⢿⡇⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⣾⣶⠆⠀⠈⠛⠛⠁⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠀⢀⠃
⠀⠀⠐⠿⠾⠿⠂⠈⠀⣀⠀⠀⠀⠀⠀⠠⡄⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠠⠘
⠀⠀⠀⠸⢆⡀⠀⠀⠀⠉⣀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠸⣶⣀⢀⡀⠀⢠⡄⠀⠀⣠⣶⣿⣿⡆
⠀⠀⠀⢰⡌⠃⠀⠀⣠⠀⣭⠀⠀⢀⡀⠠⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠉⠉⠀⠀⠘⢷⣤⣴⣿⣿⣿⠟
⠀⠀⠀⠘⠃⠀⠀⠀⠉⠀⠛⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⠘⠃⠀⠐⠀⠋⠙⠉⠉⠓

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⢰⣦⠀⠀⠀⠀⠀⠀⠐⡀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢀⣦
⠀⠀⠀⢐⣿⣷⣆⠀⠀⠀⠀⢜⠋⠵⡂⠀⠀⠀⠀⢸⣿⣇⠀⠀⠀⠀⠠⠝⣂⠀⠀⠀⠀⠀⣔⠫⢂
⠀⠀⠀⣼⣻⢿⣿⡀⠀⠀⢠⣈⡉⠒⠪⡄⠀⠀⠀⣾⣟⣿⡀⠀⠀⠀⣐⡻⠖⠂⠀⠀⠀⢸⠂⠬⠤⡀
⠀⠀⠠⠾⠿⣿⠯⠆⠀⠀⠙⠖⢶⡐⠉⠓⠀⠀⣨⣽⣿⢿⣧⠀⠀⠤⠵⠒⣉⡭⠀⠀⠀⢦⣍⣉⣩⡵
⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈

⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⢈⣇⠀⠀⠀⠀⠀⠀⡀⠄⠀⠀⠀⠀⠀⣴⣷⡀⠀⠀⠀⠀⠀⠸⠦⡀
⠀⠀⠀⠀⢠⣗⠀⠀⠀⠀⠀⢀⣼⣿⡄⠀⠀⠀⢀⣐⠦⣨⠄⠀⠀⠀⢀⣿⣿⣷⡀⠀⠀⠀⠤⠶⣛⢄
⠀⠀⠀⠀⣗⣒⡢⠀⠀⠀⠀⣰⣷⣿⣧⠀⠀⠀⠠⠍⠀⠀⣊⠀⠀⢀⣼⣿⣿⣿⣀⠀⠀⠀⣽⢻⣚⣭⠄
⠀⠀⠀⡼⣚⣖⣺⣧⠀⠀⠀⠉⢹⣿⠉⠁⠀⠀⠀⠈⠧⠏⠀⠀⠀⠤⢿⢿⡿⣿⠧⠀⠀⠈⠉⠙⠞⠁

⠀⠀⠀⠀⢀⣾⣆⠀⠀⠀⠀⠀⠀⠀⢰⡄⠀⠀⠀⠀⠀⠀⠀⣼⣷⡀⠀⠀⠀⠀⠀⠀⣰⣷⡄
⠀⠀⠀⠀⣻⣿⣿⡃⠀⠀⠀⠀⠀⢀⣿⣷⠀⠀⠀⠀⠀⠀⣨⣿⣿⣇⠀⠀⠀⠀⠀⣴⣿⣿⣿⡄
⠀⠀⠀⢾⣿⣿⣿⣿⠄⠀⠀⠀⠀⣸⣿⣿⡆⠀⠀⠀⠀⢀⣽⣿⣿⣿⡀⠀⠀⠀⢠⣾⣿⣿⣿⣧
⠀⠀⠰⠿⣿⣿⣿⡿⠧⠀⠀⠀⢠⣿⣿⣿⣿⠀⠀⠀⠀⣨⣿⣿⣿⣿⣇⠀⠀⢀⣴⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠻⠀⠀⠀⠀⠀⠀⠀⠈⠙⠋⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠗


⠀⠀⠀⠀⠀⣴⡄⠀⠀⠀⠀⠀⠀⢀⣴⣆⠀⠀⠀⠀⠀⠀⠀⢠⣆⠀⠀⠀⠀⠀⠀⠀⢠⣦
⠀⠀⠀⠀⣾⣿⣿⠄⠀⠀⠀⠀⠀⣺⣿⣿⡗⠀⠀⠀⠀⠀⠠⣿⣿⠆⠀⠀⠀⠀⠀⠠⣿⣿⡷
⠀⠀⠀⣰⣿⣿⣿⣷⡀⠀⠀⠀⢘⣿⣿⣿⣟⠂⠀⠀⠀⠀⢸⣿⣿⡗⠀⠀⠀⠀⠀⣾⣿⣿⣿⡆
⠀⠀⢀⣾⣿⣿⣿⣿⣆⠀⠀⠀⣻⣿⣿⣿⣿⡓⠀⠀⠀⠀⣿⣿⣿⣿⡂⠀⠀⠀⢠⣾⣿⣿⣿⣧
⠀⠀⠀⠈⠉⢿⠉⠉⠀⠀⠀⠈⠛⠛⠻⠟⠛⠛⠀⠀⠀⠈⠉⠹⡏⠉⠁⠀⠀⠀⠀⠉⠉⡟⠉⠁

⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⣠⡦⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⡦⠀⠀⠀⠀⢀⣤
⠀⠀⣾⣿⡄⠀⠀⢀⣟⡀⠀⠀⠠⠄⡂⠀⠀⢀⣦⡀⠀⠀⠀⣌⣻⣿⣧⡤⠀⠀⠀⠀⣾⣷⠀⠀⠀⠀⠀⠠⣟⡀⠀⠀⠀⠀⣧
⠀⢠⣿⣿⣧⠀⠀⠴⣯⡥⠀⠀⠂⠀⢁⠀⠀⣾⣿⣧⠀⠀⠲⣶⣿⣿⣽⡶⠁⡂⠀⢸⣿⣿⡇⠀⠀⠀⠀⡌⢕⠠⠀⠀⠀⣼⣿⣆
⠀⣸⣿⣿⣿⠀⠐⠂⠓⠖⠀⠀⠅⢠⠸⠀⣸⣿⣿⣿⡀⠀⢀⣀⠀⠿⠀⠀⠀⡇⠀⠿⢿⡿⠿⠀⠀⠀⠌⠀⢆⠀⢀⠀⣰⣿⣿⣿⡄
⠐⠟⢻⣿⠛⠃⠘⢣⣁⣴⠃⠀⢀⠃⠀⠠⣿⣿⣿⣿⠧⠀⡵⡺⠄⠀⠀⠀⠀⡇⠀⠀⠘⠃⢀⠀⠈⢀⠈⠀⡿⠀⠀⢠⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠈⠿⠇⠀⢀⣾⣷⡀⠀⠀⠀⣿⠀⠀⠠⣚⣝⣂⠀⠀⠀⠀⠃⠀⠀⠀⠠⣌⠁⣀⢉⡤⠀⠀⢀⣤⡀⠉⠉⠿⠉
⠀⠀⢼⡓⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣧⠀⠀⠀⠀⠀⠀⠨⢿⣗⣿⠀⠀⠀⢻⣿⠃⠀⠀⠠⢄⠤⠔⠠⠐⠄⢀⡤⠖⠢⠄
⠀⠐⣺⣍⡑⠀⠀⢀⡲⠄⠀⠉⠹⠏⠉⠀⠀⠀⠀⠀⠀⠋⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠒⠤⠤⠒⠄⠒⠀⢀⠔⠋⠓⠢⠀⢠⡀
⠀⣈⢽⡗⠬⠤⢀⣙⣒⣒⡀⠀⠀⣠⢖⢰⠃⢠⠀⠰⠀⢠⠇⠀⠀⠀⠀⠀⠀⠒⠒⣤⡄⠀⠀⠀⠀⠀⠀⠀⢠⠔⠋⠓⠢⠀⢺⠓
⠀⠒⣿⣿⡉⠀⠴⠄⣒⣪⠥⠀⠀⡏⡁⡟⡞⢸⣤⡇⢺⣞⡰⠶⡆⣞⡅⠷⠀⠀⣸⠈⡇⢼⠣⡏⣿⠠⠀⠀⠀⠀⠀⠀⠀⡌⢸⠀⠆
⠀⠀⠁⠀⠀⠀⢀⠀⠋⠀⠀⠀⠀⠃⠀⠀⠁⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠁⠀⠠⠃⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠠⣤⠄⠰⠁⢸⡤⠴
⠀⠀⠀⠀⠀⢴⣿⣷⠄⠀⠀⠀⠀⣰⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡀⠀⠀⠒⠶⠖⠀⠀⠸⠇
⠀⠀⠀⠀⠐⣺⣿⣿⡿⠂⠀⠀⣸⣿⣿⣿⡄⠀⠀⠀⠀⠀⠔⠒⠄⠀⠀⠀⣀⠀⠀⠀⢸⠀⠀⠀⣼⡶⣷⠀⠀⠂⠘⠠⠂
⠀⠀⠀⠈⠻⠿⢿⡿⠟⠁⠀⢠⣾⣿⣿⣿⣧⠀⠀⠀⠀⢼⠃⠀⠑⡀⠀⢠⣿⡀⠀⠀⣽⠀⠀⠰⣷⣶⣾⠂⠠⠀⠀⠀⠒⠀⣀
⠀⠀⠀⡎⠀⠀⠀⠂⠀⣀⠀⠼⠿⠿⠿⠿⠿⠃⠀⠀⠀⡋⠀⢀⢘⡇⠀⣼⣿⡇⠀⠀⡺⠀⠀⣼⣭⡤⣤⣇⠀⠀⠀⠀⠀⣺⣿⡇
⠀⠀⠐⠐⠀⠀⠀⠀⠐⠒⠀⠀⠀⠀⠀⢰⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣦⡀⠀⠀⠀⢽⣟⡶
⠀⠐⠃⠀⢄⡀⠀⠀⠁⠀⠀⠀⠀⠀⢀⣿⣿⡀⠀⠀⠒⡦⠐⠂⠀⠀⣾⣿⣿⣿⡄⠀⢠⠒⡂⠀⠀⠀⣸⣿⣿⣷⡄⠀⢐⣿⡿⢽⠄
⢀⡀⠀⠀⠀⠀⠀⡀⢀⣀⠀⠀⠀⠀⣼⣿⣿⣇⠀⠈⠁⠒⠀⣁⠀⠀⠿⠿⡿⠛⠃⢀⠉⠀⠈⠄⠀⢠⣿⣿⣿⣿⡇⠀⠒⢿⠿⡟⠃
⠈⠀⠠⡌⠐⠀⠀⠀⠀⠿⠀⠀⠀⠀⠛⢻⡛⠛⠀⡉⠀⠛⠀⠠⠀⠀⠀⠀⠁⠀⠀⡘⠀⠀⢈⡈⠀⠘⠛⠻⣿⠛⠋⠀⠀⠘⠚⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠄⠄⢒⠀⠐⠀⡄⢀⡶⠂⠀⠠⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠔⠂⠁⠀⠀⠀⠀⠀⠉⠈⠛⠣⠝⠀⠠⣄⠀⠀⠀⠍⡲⡤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠔⠊⠁⠀⠀⠀⠀⠀⠁⣀⣤⠎⠁⠀⠴⠃⢀⣀⠀⠙⢤⠀⢠⠇⠀⠀⠑⠤⡀
⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⣀⡄⢀⣢⡤⠵⠶⠛⠛⠛⠛⠻⠶⢶⡦⣥⣐⠀⡈⠀⠀⠀⡀⠀⠬⠦⡀
⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⢠⠦⠠⢞⣭⡾⠋⠉⠀⠀⠀⠀⠰⠤⠀⠀⠀⠀⠀⠈⠻⢿⣶⣅⡠⡀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠠⠂⠒⢂⠒⠈⠁⢂⣴⣿⡟⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣮⡢⡾⠆⠰⠄
⠀⠀⠀⠠⠁⠀⠀⠀⢱⡔⣵⣿⣿⡟⣡⣶⡿⠁⡀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⣿⣿⣿⣜⠾⠄⠈
⠀⠀⠠⠃⠀⠀⠀⠀⢌⣾⣿⣿⣿⣷⣿⡁⠀⠀⠙⢁⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠸⡆⠀⢿⣿⣿⣿⣆⢀⣠
⠀⠀⡄⠀⠀⠀⠀⡀⣼⣿⣿⡿⣻⣿⣿⣷⣶⣇⢀⣼⡇⠀⢀⠠⠖⠛⠉⠉⠙⠛⠛⣶⣧⣄⣸⣿⣿⣿⣿⡎⢙
⠀⠀⠀⠀⠠⠂⠀⢸⣿⣿⣿⣷⣚⢿⣿⣿⣿⣿⣿⣿⡷⣾⠟⠒⠀⢀⠀⢰⡔⠛⠃⠈⢯⡹⣿⣿⣿⣿⣿⣿⡸
⠀⢸⠀⢀⠀⠀⡟⣾⣿⣿⣿⣿⣿⣼⡿⣿⣿⣿⣿⣯⠀⢹⡤⠖⠋⢻⣦⠀⠁⢀⡀⢀⠖⡂⠈⠉⠹⣿⣿⣿⡇
⠀⠈⠀⠈⠀⢀⠃⣿⣿⣿⣿⣿⠿⡯⢉⠛⣿⣿⡿⢿⣷⣴⡠⠀⠀⢀⡝⢁⣀⠘⠃⠀⠀⠀⠀⠀⠀⠀⢿⣿⡇
⠀⢰⠀⠀⠀⠎⢀⢿⣿⣿⣧⡀⠌⠀⢀⣴⣿⣿⡇⠀⠈⠙⠁⢀⡚⠉⠈⠁⠀⠀⠀⠀⢀⣀⣠⠀⠀⠀⠈⣿⡇
⠀⠀⠈⡀⠀⠀⠀⢸⣿⣿⣣⠏⠀⠠⢿⣿⣿⣿⡷⠀⠀⠀⠀⠈⠀⠀⡀⣄⣤⡤⠐⠚⠛⠙⠁⠀⠀⠀⠀⢹⢡
⠀⠀⠂⠸⣄⠀⢀⣴⣿⡟⠁⠀⢀⠀⠀⡀⣻⣿⣿⣆⡀⠀⡀⢼⠿⡿⡏⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠘⠀⣨⣶⡿⢿⡟⠁⠀⠀⠈⠀⠀⠠⡈⣿⡀⠈⣿⠀⠄⠀⠑⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿
⠀⠀⢠⣿⡿⣫⢀⠀⡄⠀⠀⠀⠀⠀⠠⡄⢈⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻
⠀⣰⣿⡟⠰⠁⠄⠀⠀⠀⠀⢀⠐⠀⣴⣶⣾⣿⢀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⢰⣟⡅⢠⠰⠀⠀⠀⠀⣀⡄⠀⠀⠺⣿⣟⣿⣿⣿⣿⠀⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⢸⡏⡇⠀⠀⠀⠀⠀⠀⡛⠀⠀⠀⠀⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⢶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠀⢀⣠⠶⠶⣦⣄⣀⣠⣤⣤⣄⠀⠀⣠⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡿⡟⠋⠀⠀⠀⠀⠉⠉⠉⣴⡇⠈⠛⠛⢻⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠁⠀⢀⣤⠤⢤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣶⠞⠋⠀⠀⠀⠀⡙⠳⠶⣤⣄⣠⣤⣴⠿⠛⠉⢉⡉⠑⠲⣶⡾⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠃⠀⠀⠀⠀⠀⠘⠋⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠻⠃⠀⠀⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠁⠀⢀⣠⣤⣤⣤⣤⣄⣀⠀⢀⣠⣤⣤⣤⣤⣄⡀⠀⠀⠀⠀⠀⢀⣤⣤⣀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢛⡿⠋⣥⡆⠀⠀⠀⠉⠙⠛⠛⠉⠁⠀⠀⣴⡏⠙⠳⢦⣤⣀⣀⣾⡏⠀⠈⠹⣟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠋⠀⠀⠀⠀⠹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡏⠁⢀⣠⠴⠒⠛⠛⠳⣦⣀⠀⠀⠀⣀⣤⠶⠶⠶⢤⣄⡀⠀⠀⠀⠀⠀⣀⣤⡤⠤⣄⣀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣹⠏⠉⢴⣦⠀⠀⠀⠀⠀⠙⠓⠶⠛⣿⠄⠀⠀⠀⠀⠈⠙⠳⢤⣤⣴⠾⣿⡧⠀⠀⠀⠈⠙⢶⡶⠾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⢀⣴⠋⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣀⡀⠀⠈⣧⡀
⠀⠀⠀⠀⠀⠀⠘⠿⠿⠶⠞⢋⡉⠉⠛⠿⣷⣦⣀⣀⣀⣀⣤⣤⣤⣤⣄⣀⡀⠀⠀⣀⣤⣴⣶⣶⣦⣤⣄⣀⣠⣴⣾⠟⢋⣭⠉⠉⠛⠛⠿⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠉⠛⠛⠛⠉⢁⣀⡤⡽⠉⠛⠛⠛⠛⠛⢹⣅⡀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠈⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠒⠉⠁⠤⠤⠧⢄⣀⡀⠀⠀⠀⢸⡍⠙⠳⠶⣤⣄⣀⡀
⠛⠻⠶⠶⠤⣤⣤⣀⣀⣀⣀⣤⠤⠤⠖⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠒⠒⠒⠒⠒⠒⠂⠀⠀⠉⠉

⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠉⠀⠲⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠰⠶⣠⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠘⠃
⠀⠀⠀⠀⠀⠀⠈⠀⠘⠀⠺⠂⠰⠂⠰⠗⠀⠒⠀⠘⠃⠀⠀⠀⠀⠈⠁⠒⠀⣤⠄⢠⠄⠰⠖⠈⠁


⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠒⢀⣠⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣘⠿⠻⠟⣛⣡⣆⠀⠀⠀⠀⠀⠀⠀⢠⣶⣍⣫⣅⣡⣴⣷⡄
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠆⠀⠀⠀⠀⠀⠀⣈⡙⠛⠙⠛⢋⠭⢲⠃
⠀⠀⠀⠀⠀⠀⠀⠘⠻⠿⠟⠿⢛⣉⡵⠀⠀⠀⠀⠀⠀⠀⠉⣓⠛⠝⠊⠛⢈⣠⠄⠀⠀⠀⡠
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠙⠛⠟⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠾⠿⠛⠁⠀⠀⠀⠀⠄⠠⠀⣄
⠀⠀⠀⠀⠛⠉⠂⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠝⢳⠒⡓⢛⠉⠅⣀
⠀⠀⠁⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠰⠶⢦⣤⢤⣤⠶⢚⡉
⠀⠀⠀⠀⠂⠀⠀⠀⢀⡅⠀⠀⠀⠀⠀⠀⢻⡿⢿⡿⢿⠟⠓⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠐⠀⠒⠈⠁
⠀⠈⢀⡀⠀⠀⠀⢀⠔⠀⠀⠀⠀⠀⠀⠰⣄⣠⣄⣀⣤⣠⡶
⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠽⠿⠿⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄
⠀⠀⠀⠀⠀⢠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⢀⡠⠖⠃
⠀⠀⠀⠀⠀⠀⠩⡟⢳⣄⡀⠀⠀⠀⠀⢀⢀⣀⡤⠶⠖⠛⠛⠛⠋⠀⠀⠀⠀⠀⢀⢀⣤⡴⠖⠚⠋⠁⠀⠀⠀⣠⠞⠁⠀⣀⣠⡞⠉⠀⠀⠀⣀⡤⠔⠃
⠀⠀⠀⠀⠀⠀⠐⡗⠀⠹⡉⢳⣶⣶⣾⠟⠭⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠖⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⣧⣤⢴⠞⢻⡟⠒⠒⠒⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢡⠈⠘⢿⢫⠽⠒⠶⡤⣄⣀⣠⣠⣴⣶⠯⠕⠒⠀⠀⠀⠀⡀⣀⣠⣤⣤⣤⡞⠛⡟⠁⢇⠞⠀⢸⠄
⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠘⣄⠀⠀⠳⣍⠑⠀⠅⠀⠺⠝⢿⡿⢿⣋⠛⢻⠿⣿⣿⢯⣽⡋⠀⠀⠀⠻⣽⣽⠓⣾⡟
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠸⣄⠀⠀⠉⢣⡄⠆⠀⠟⠀⠀⠙⢶⣷⡄⠈⠁⠀⡨⠟⠶⣬⣄⣀⠀⠀⢸⠢⠘⡙⠀⠀⠀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠙⢄⠀⠀⠀⠀⠃⠀⠠⠀⠀⠀⠀⠈⠻⣶⣠⠞⠁⠀⠀⠀⠀⠉⠁⠀⠊⠀⡘⠁⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠱⣤⠀⠀⠀⠀⠸⠆⠀⠀⠀⠀⡠⠘⢣⡀⠀⠀⠀⠀⠀⠀⠀⠌⣠⠎⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⠀⠀⠀⠈⠒⠦⠤⠤⢤⠤⠄⠚⠃⢀⢀⢀⡉⠢⢀⠀⢀⡀⢀⡬⠘⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣾⣿⣶⠃⠀⠀⠀⠀⠀⠀⠀⠨⡄⠀⠀⠐⣾⣿⣿⠒⠀⠀⠀⠉⢉⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣶⣷⣖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠙⠏⠁⠀⠀⠀⠀⣤⠀⣀⠀⠐⢄⠀⠀⠘⠉⠋⠁⠀⠀⠀⠴⠃⠀⠀⢀⢰⠀⡀⠀⠀⠀⠀⠀⠀⠈⠝⠛⠍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣻⣿⣿⣧⡄⠀⠈⠲⣄⠀⠀⠀⢀⣀⠔⠉⠀⠀⠀⠐⣾⣿⣿⡖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠹⠻⠏⠓⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠙⠇⠉

⠀⠀⠀⡀
⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⣐⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠂⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠘⠂⠅⠀⠀⠨⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠄⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⣏⠝⠀⠀⠀⠀⠀⠀⠀⢠
⠀⢀⠀⠀⠀⠀⠴⠀⠀⠀⠀⠀⠀⠙⠀⠀⡄⠀⠈⠔⠀⠀⠀⠂⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠁⠀⠰⢀⣇⠴⠀⠀⠀⠀⢀⠄⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢃⠻⡼⢃⠃⠀⠈⠀⢀⠀⢀⠄⠀⠀⠀⠀⠀⠀⢠⡀⠐⠂⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠃⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⡨⡾⢷⢀⢀⡀
⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⡀⠀⠀⠀⡀⠀⢀⠐⠽⠏⢂⡀
⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃
⠀⠀⠀⣂⠤⣐⠀⠀⠰⠀⠈⠲⢄⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠈⠎⠒⠱⠁⠀⢀⠴⡄⠀⠀⠉⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⠐⠁⠀⠐⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣼⣿⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⠧⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣿⢶⣬⣹⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠀⣠⡌⠳⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣥⣶⣾⣿⣿⣦⣀⠀⣰⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣂⠉⠉⣹⡟⠛⣿⣿⣿⡿⢿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡴⠋⠁⢀⣶⡿⠿⣿⣿⣶⣦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣞⣛⠉⠸⣆⢰⣿⣿⣦⣤⠟⠿⠦⢽⣭⣽⡆⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡿⣿⣿⣿⣧⣤⣍⣾⢿⣟⣋⣡⣴⣞⣁⠲⠾⠛⠀⢸⡷⣤⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠛⠻⢛⣿⠿⠋⣀⣤⡼⣆⡀⠈⢉⣷⣶⡶⢯⣁⣴⠏⠀⢀⣠⣾⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣾⣤⠔⠛⠁⠀⢸⣿⣿⣿⣉⠙⠋⢫⣍⡉⣉⢫⣿⣿⣶⣿⣿⣿⣿⡛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡶⠶⠒⠛⣛⠋⠀⠸⣆⠀⣶⣶⣿⢿⣿⣿⣿⠟⠛⢿⣿⣿⣿⣴⡾⣏⣛⠋⣩⣿⣷⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠻⠶⣦⡾⠁⣀⣴⣶⣿⣾⣿⣿⣿⣿⢿⣿⣿⠆⠠⠞⢿⣄⣹⣉⠻⢻⡿⢿⠟⡏⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢸⣧⡞⣿⣿⢻⣿⡿⢛⣛⣿⣿⣋⣿⣿⣿⣶⣤⣄⣄⠈⠉⣱⠖⠀⠐⠛⣉⣊⡙⠷⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠚⣁⠈⣭⠶⠛⠁⠀⣸⣿⠉⢙⣿⣉⣀⣀⢉⡻⣿⣯⠵⠛⢤⣦⣶⣄⣼⡿⢫⡏⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣤⠐⠚⠛⠂⠀⠉⢷⡀⠀⣠⣾⠾⠟⠋⡉⠛⢿⣶⣉⡉⠉⠁⠙⢷⣶⡄⢀⡉⠉⠻⠟⠒⠚⠓⢂⣈⣰⣶
⠀⠀⠀⠀⠀⣶⢰⣶⣤⢀⠀⠘⢿⣨⣧⣿⣶⡄⢲⣼⡳⣮⠛⠁⢀⣴⣟⣿⣦⠀⠙⢿⣷⣷⠀⠀⠀⡼⠻⣿⣿⣶⣦⣼⣦⣼⠟⠛⠉⠙⠃
⠀⠀⠀⠀⢰⣇⣾⡿⢻⡟⠀⠀⠀⠈⠁⢾⣿⣶⣿⠟⠉⠀⠴⣾⣟⣿⡧⣿⣿⡇⠀⠀⠙⣷⣶⣶⡈⢦⣠⠟⠈⠙⢿⣿⠙⠉⠀⠀⠀⠀⠀⡀⢠⣤⠆
⠀⠀⠀⠀⠀⡿⠿⣡⡟⠀⣠⣤⣤⡄⠀⣀⣾⡿⠋⠀⣴⣤⣾⣿⣿⣿⣄⣼⣿⣧⣤⠀⠀⠙⠷⢿⣿⣶⢶⣶⣦⣀⠀⡉⠛⠶⢄⣀⣀⣤⢾⣿⣌⣿⡇
⠀⠀⠀⠀⢸⠃⢀⡿⣴⣆⢻⣿⣿⣷⠞⠉⠁⢀⣴⣷⡼⣿⣯⣿⣄⣨⣀⣨⣿⡿⢷⣴⣾⡄⢠⣤⣼⡟⠳⣌⠀⣹⠿⠿⢷⣷⣆⣩⣉⣹⣿⡾⠟⣿⣅⣠⠄
⠀⠀⠀⠀⢼⡀⣸⠃⠘⣿⡌⣿⣿⣿⡆⢷⣴⡾⠛⠛⠿⣼⣿⣿⣿⣿⣿⠟⠛⠛⠛⢻⣿⠃⣿⣿⣿⡏⢀⡼⠃⠀⠀⠀⠀⢹⡿⣛⣿⢿⡟⠁⢠⡿⡶⠄
⠀⠀⠀⠀⢸⡇⠹⣦⠔⢻⡷⠘⠉⠉⣉⣴⠿⣥⣾⣿⡿⠿⣿⣿⣿⡏⠀⠀⣀⣀⡀⢸⠿⠠⢿⣿⣿⣡⣿⣵⣿⠿⢿⣦⠀⢸⣀⣿⣠⡾⢃⡄⣾
⠀⠀⢀⣤⢾⣧⠀⠹⣷⣾⣤⣴⣿⡟⠛⢻⣿⣿⣿⣏⠀⠀⠰⣏⢿⡇⣠⡿⠟⠛⢿⡷⠤⠤⣤⣬⣿⣿⣽⡏⠀⠀⠈⣿⡇⣼⡤⠾⢟⣵⣊⣼⣃⡀
⠀⠀⠚⣸⣿⣿⢆⠀⢹⢾⣿⣿⠞⠃⠀⢀⣿⣿⣿⢡⠀⠀⠀⣸⡜⢻⣿⠀⠀⠀⣼⠑⠀⠀⢀⡝⣿⣿⢿⡧⠀⠶⢀⣿⣿⣥⠶⢚⣿⣿⣫⣄⢈⡉⠁⣀
⠀⠀⠀⠀⠙⠁⠀⣿⣧⣼⡛⣁⡀⠆⡀⣼⣿⣿⣿⡷⣦⠰⠀⣿⡇⢻⣿⠧⡘⠂⢿⡇⡦⠀⠀⠙⣿⡷⣄⠰⢦⣀⠶⠀⣼⣷⡿⠟⠉⡍⠈⣿⠿⠙⠃⠈
⠀⠀⠀⠀⠀⣾⢻⡉⠻⣍⠛⠿⣿⣩⣴⠋⢉⣹⡇⠀⠁⠑⠊⠉⠀⢸⡍⣳⣴⣶⡾⠿⢆⢰⡆⠺⣿⣿⣿⣷⣶⣄⣠⠞⢁⡠⠝⠃⣼⠶⠄
⠀⠀⠀⠀⢸⡇⠘⢃⡀⣘⣦⣀⡀⠉⣍⠓⠛⠿⣿⣦⣄⣀⣀⣤⣠⣿⣿⣯⣿⣿⣇⣀⡜⠉⢣⣄⣾⣿⣿⣿⡿⠟⠋⠉⠀⠀⠀⢠⣧⣤⡀⠈
⠀⠀⠀⠀⣼⢋⡴⠋⣽⣿⣿⣿⠟⡄⣿⢹⢲⡄⠀⠈⠉⠙⠟⠿⠿⢿⡿⠿⠿⠿⠟⠛⠛⠀⠛⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡿⠃⠀⡻
⠀⠀⠀⢠⡟⣹⡇⠀⢿⡻⢹⠀⠀⠀⣿⢸⢸⡇⣠⡄⣀⠀⡀⠀⠀⠀⠀⣶⠸⠆⣶⠀⠀⠀⠀⠀⢀⢀⡄⣠⣤⣤⢐⣶⠻⡆⢠⡿⠠⢤⠔⠈
⠀⠀⠀⢸⣿⠋⢷⡀⢠⠃⣆⣀⠀⠀⠉⠘⠺⠇⠏⠀⣏⠀⡇⠘⡇⣷⠀⣿⠀⠀⢿⢸⡆⡇⠁⣇⠉⣶⡇⢽⠿⠿⠛⠛⠀⢀⡞⠁⢀⡾
⠀⠀⠀⢸⡇⠀⣸⡿⠞⠀⠀⠉⠙⠓⠶⠦⢤⣤⣀⣀⠀⠀⠁⠀⠁⠟⠀⠉⠀⠀⠙⠈⠁⠉⠀⠉⠀⠀⠀⣀⢠⣤⡤⠶⠚⠁⠹⣠⠞⠁
⠀⠀⠀⠈⢿⣠⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠦⣄⡠⢦⣤⣤⣤⣠⣄⣀⣤⣄⡠⠲⠶⠲⠖⠋⠉
⠀⠀⠀⠀⠈⠉