**
==\@#$%$%^&*()_+||+_)(**&^^%$$##((**&&^^^^^%%^^66666^^^^%%R%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$#$%^U*I(*$E!~!~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~%^%&(*&%^%&(*_)+_|)O&^%^%$$%$%^%^^&^&&^&*&*(**()(_+_+|HNEQW!@##$%$&^&*U(*())(*(*(*))())__)(************))((U&**(_)+___*&**((()__+_+_+*^^&*)_+_)*&*&*((_)_+|_+&**U*O)&@#$%T^&&&&&&&&*(Y^R%&^*&*()()(()((()))_*&%%%$%^%^&^(*()()((((**************^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
**
==\@#$%$%^&*()_+||+_)(**&^^%$$##((**&&^^^^^%%^^66666^^^^%%R%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$#$%^U*I(*$E!~!~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~%^%&(*&%^%&(*_)+_|)O&^%^%$$%$%^%^^&^&&^&*&*(**()(_+_+|HNEQW!@##$%$&^&*U(*())(*(*(*))())__)(************))((U&**(_)+___*&**((()__+_+_+*^^&*)_+_)*&*&*((_)_+|_+&**U*O)&@#$%T^&&&&&&&&*(Y^R%&^*&*()()(()((()))_*&%%%$%^%^&^(*()()((((**************^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
**
==\@#$%$%^&*()_+||+_)(**&^^%$$##((**&&^^^^^%%^^66666^^^^%%R%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$#$%^U*I(*$E!~!~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~%^%&(*&%^%&(*_)+_|)O&^%^%$$%$%^%^^&^&&^&*&*(**()(_+_+|HNEQW!@##$%$&^&*U(*())(*(*(*))())__)(************))((U&**(_)+___*&**((()__+_+_+*^^&*)_+_)*&*&*((_)_+|_+&**U*O)&@#$%T^&&&&&&&&*(Y^R%&^*&*()()(()((()))_*&%%%$%^%^&^(*()()((((**************^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
**
==\@#$%$%^&*()_+||+_)(**&^^%$$##((**&&^^^^^%%^^66666^^^^%%R%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$#$%^U*I(*$E!~!~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~%^%&(*&%^%&(*_)+_|)O&^%^%$$%$%^%^^&^&&^&*&*(**()(_+_+|HNEQW!@##$%$&^&*U(*())(*(*(*))())__)(************))((U&**(_)+___*&**((()__+_+_+*^^&*)_+_)*&*&*((_)_+|_+&**U*O)&@#$%T^&&&&&&&&*(Y^R%&^*&*()()(()((()))_*&%%%$%^%^&^(*()()((((**************^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
**
==\@#$%$%^&*()_+||+_)(**&^^%$$##((**&&^^^^^%%^^66666^^^^%%R%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$#$%^U*I(*$E!~!~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~%^%&(*&%^%&(*_)+_|)O&^%^%$$%$%^%^^&^&&^&*&*(**()(_+_+|HNEQW!@##$%$&^&*U(*())(*(*(*))())__)(************))((U&**(_)+___*&**((()__+_+_+*^^&*)_+_)*&*&*((_)_+|_+&**U*O)&@#$%T^&&&&&&&&*(Y^R%&^*&*()()(()((()))_*&%%%$%^%^&^(*()()((((**************^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
**
==\@#$%$%^&*()_+||+_)(**&^^%$$##((**&&^^^^^%%^^66666^^^^%%R%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$#$%^U*I(*$E!~!~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~%^%&(*&%^%&(*_)+_|)O&^%^%$$%$%^%^^&^&&^&*&*(**()(_+_+|HNEQW!@##$%$&^&*U(*())(*(*(*))())__)(************))((U&**(_)+___*&**((()__+_+_+*^^&*)_+_)*&*&*((_)_+|_+&**U*O)&@#$%T^&&&&&&&&*(Y^R%&^*&*()()(()((()))_*&%%%$%^%^&^(*()()((((**************^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
**
==\@#$%$%^&*()_+||+_)(**&^^%$$##((**&&^^^^^%%^^66666^^^^%%R%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$#$%^U*I(*$E!~!~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~%^%&(*&%^%&(*_)+_|)O&^%^%$$%$%^%^^&^&&^&*&*(**()(_+_+|HNEQW!@##$%$&^&*U(*())(*(*(*))())__)(************))((U&**(_)+___*&**((()__+_+_+*^^&*)_+_)*&*&*((_)_+|_+&**U*O)&@#$%T^&&&&&&&&*(Y^R%&^*&*()()(()((()))_*&%%%$%^%^&^(*()()((((**************^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^