Av(13452, 13542, 23451, 23541, 32451, 32541)
Counting Sequence
1, 1, 2, 6, 24, 114, 596, 3292, 18800, 109686, 649230, 3881672, 23377286, 141548536, 860566128, ...
This specification was found using the strategy pack "Point And Row Placements Tracked Fusion Tracked Component Fusion Req Corrob Symmetries" and has 200 rules.
Finding the specification took 15392 seconds.
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\(\begin{align*}
F_{0}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{2}\! \left(x \right)\\
F_{1}\! \left(x \right) &= 1\\
F_{2}\! \left(x \right) &= F_{3}\! \left(x \right)\\
F_{3}\! \left(x \right) &= F_{21}\! \left(x \right) F_{4}\! \left(x \right)\\
F_{4}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{5}\! \left(x \right)+F_{67}\! \left(x \right)\\
F_{5}\! \left(x \right) &= F_{21}\! \left(x \right) F_{6}\! \left(x \right)\\
F_{6}\! \left(x \right) &= F_{4}\! \left(x \right)+F_{7}\! \left(x \right)\\
F_{7}\! \left(x \right) &= F_{8}\! \left(x , 1\right)\\
F_{9}\! \left(x , y\right) &= -\frac{-F_{8}\! \left(x , y\right)+F_{8}\! \left(x , 1\right)}{-1+y}\\
F_{9}\! \left(x , y\right) &= F_{10}\! \left(x , y\right)\\
F_{10}\! \left(x , y\right) &= -\frac{-y F_{11}\! \left(x , y\right)+F_{11}\! \left(x , 1\right)}{-1+y}\\
F_{11}\! \left(x , y\right) &= F_{12}\! \left(x \right)+F_{87}\! \left(x , y\right)\\
F_{12}\! \left(x \right) &= F_{13}\! \left(x \right)\\
F_{13}\! \left(x \right) &= F_{14}\! \left(x \right) F_{21}\! \left(x \right)\\
F_{14}\! \left(x \right) &= F_{15}\! \left(x \right)+F_{22}\! \left(x \right)+F_{4}\! \left(x \right)\\
F_{15}\! \left(x \right) &= F_{16}\! \left(x \right)\\
F_{16}\! \left(x \right) &= F_{17}\! \left(x \right) F_{21}\! \left(x \right)\\
F_{17}\! \left(x \right) &= F_{18}\! \left(x , 1\right)\\
F_{19}\! \left(x , y\right) &= F_{18}\! \left(x , y\right) F_{20}\! \left(x , y\right)\\
F_{19}\! \left(x , y\right) &= F_{8}\! \left(x , y\right)\\
F_{20}\! \left(x , y\right) &= y x\\
F_{21}\! \left(x \right) &= x\\
F_{22}\! \left(x \right) &= -F_{4}\! \left(x \right)-F_{62}\! \left(x \right)+F_{23}\! \left(x \right)\\
F_{23}\! \left(x \right) &= \frac{F_{24}\! \left(x \right)}{F_{21}\! \left(x \right)}\\
F_{24}\! \left(x \right) &= F_{25}\! \left(x \right)\\
F_{25}\! \left(x \right) &= -F_{26}\! \left(x \right)+F_{4}\! \left(x \right)\\
F_{26}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{27}\! \left(x \right)\\
F_{27}\! \left(x \right) &= F_{28}\! \left(x \right)\\
F_{28}\! \left(x \right) &= F_{21}\! \left(x \right) F_{29}\! \left(x \right)\\
F_{29}\! \left(x \right) &= F_{30}\! \left(x \right)+F_{43}\! \left(x \right)\\
F_{30}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{31}\! \left(x \right)\\
F_{31}\! \left(x \right) &= F_{32}\! \left(x \right)\\
F_{32}\! \left(x \right) &= F_{21}\! \left(x \right) F_{33}\! \left(x \right)\\
F_{33}\! \left(x \right) &= F_{34}\! \left(x \right)+F_{35}\! \left(x \right)\\
F_{34}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{21}\! \left(x \right)\\
F_{35}\! \left(x \right) &= F_{31}\! \left(x \right)+F_{36}\! \left(x \right)\\
F_{36}\! \left(x \right) &= F_{37}\! \left(x \right)+F_{38}\! \left(x \right)+F_{42}\! \left(x \right)\\
F_{37}\! \left(x \right) &= 0\\
F_{38}\! \left(x \right) &= F_{21}\! \left(x \right) F_{39}\! \left(x \right)\\
F_{39}\! \left(x \right) &= F_{40}\! \left(x \right)+F_{41}\! \left(x \right)\\
F_{40}\! \left(x \right) &= F_{21}\! \left(x \right)\\
F_{41}\! \left(x \right) &= F_{36}\! \left(x \right)\\
F_{42}\! \left(x \right) &= F_{21}\! \left(x \right) F_{31}\! \left(x \right)\\
F_{43}\! \left(x \right) &= F_{27}\! \left(x \right)+F_{44}\! \left(x \right)\\
F_{44}\! \left(x \right) &= F_{37}\! \left(x \right)+F_{45}\! \left(x \right)+F_{58}\! \left(x \right)\\
F_{45}\! \left(x \right) &= F_{21}\! \left(x \right) F_{46}\! \left(x \right)\\
F_{46}\! \left(x \right) &= F_{47}\! \left(x \right)+F_{48}\! \left(x \right)\\
F_{47}\! \left(x \right) &= F_{21}\! \left(x \right)+F_{36}\! \left(x \right)\\
F_{48}\! \left(x \right) &= F_{49}\! \left(x \right)+F_{51}\! \left(x \right)\\
F_{49}\! \left(x \right) &= F_{37}\! \left(x \right)+F_{45}\! \left(x \right)+F_{50}\! \left(x \right)\\
F_{50}\! \left(x \right) &= F_{21}\! \left(x \right) F_{27}\! \left(x \right)\\
F_{51}\! \left(x \right) &= F_{37}\! \left(x \right)+F_{52}\! \left(x \right)+F_{53}\! \left(x \right)+F_{57}\! \left(x \right)\\
F_{52}\! \left(x \right) &= 0\\
F_{53}\! \left(x \right) &= F_{21}\! \left(x \right) F_{54}\! \left(x \right)\\
F_{54}\! \left(x \right) &= F_{55}\! \left(x \right)+F_{56}\! \left(x \right)\\
F_{55}\! \left(x \right) &= F_{49}\! \left(x \right)\\
F_{56}\! \left(x \right) &= F_{51}\! \left(x \right)\\
F_{57}\! \left(x \right) &= F_{21}\! \left(x \right) F_{44}\! \left(x \right)\\
F_{58}\! \left(x \right) &= F_{21}\! \left(x \right) F_{59}\! \left(x \right)\\
F_{59}\! \left(x \right) &= F_{60}\! \left(x \right)+F_{61}\! \left(x \right)\\
F_{60}\! \left(x \right) &= F_{27}\! \left(x \right)+F_{49}\! \left(x \right)\\
F_{61}\! \left(x \right) &= F_{44}\! \left(x \right)+F_{51}\! \left(x \right)\\
F_{62}\! \left(x \right) &= F_{21}\! \left(x \right) F_{63}\! \left(x \right)\\
F_{63}\! \left(x \right) &= \frac{F_{64}\! \left(x \right)}{F_{21}\! \left(x \right)}\\
F_{64}\! \left(x \right) &= F_{65}\! \left(x \right)\\
F_{65}\! \left(x \right) &= \frac{F_{66}\! \left(x \right)}{F_{21}\! \left(x \right)}\\
F_{66}\! \left(x \right) &= -F_{37}\! \left(x \right)-F_{67}\! \left(x \right)+F_{25}\! \left(x \right)\\
F_{67}\! \left(x \right) &= F_{21}\! \left(x \right) F_{68}\! \left(x \right)\\
F_{68}\! \left(x \right) &= F_{69}\! \left(x , 1\right)\\
F_{69}\! \left(x , y\right) &= F_{4}\! \left(x \right)+F_{70}\! \left(x , y\right)\\
F_{70}\! \left(x , y\right) &= F_{37}\! \left(x \right)+F_{71}\! \left(x , y\right)+F_{73}\! \left(x , y\right)+F_{85}\! \left(x , y\right)\\
F_{71}\! \left(x , y\right) &= F_{21}\! \left(x \right) F_{72}\! \left(x , y\right)\\
F_{72}\! \left(x , y\right) &= -\frac{y \left(-F_{8}\! \left(x , y\right)+F_{8}\! \left(x , 1\right)\right)}{-1+y}\\
F_{73}\! \left(x , y\right) &= F_{20}\! \left(x , y\right) F_{74}\! \left(x , y\right)\\
F_{74}\! \left(x , y\right) &= F_{69}\! \left(x , y\right)+F_{75}\! \left(x , y\right)\\
F_{75}\! \left(x , y\right) &= y F_{76}\! \left(x , y\right)\\
F_{76}\! \left(x , y\right) &= F_{37}\! \left(x \right)+F_{77}\! \left(x , y\right)+F_{79}\! \left(x , y\right)+F_{81}\! \left(x , y\right)+F_{82}\! \left(x , y\right)\\
F_{77}\! \left(x , y\right) &= F_{21}\! \left(x \right) F_{78}\! \left(x , y\right)\\
F_{78}\! \left(x , y\right) &= -\frac{-y F_{11}\! \left(x , y\right)+F_{11}\! \left(x , 1\right)}{-1+y}\\
F_{79}\! \left(x , y\right) &= F_{80}\! \left(x , y\right)\\
F_{80}\! \left(x , y\right) &= F_{20}\! \left(x , y\right) F_{76}\! \left(x , y\right)\\
F_{81}\! \left(x , y\right) &= F_{21}\! \left(x \right) F_{69}\! \left(x , y\right)\\
F_{82}\! \left(x , y\right) &= F_{21}\! \left(x \right) F_{83}\! \left(x , y\right)\\
F_{83}\! \left(x , y\right) &= F_{84}\! \left(x , y\right)\\
F_{84}\! \left(x , y\right) &= -\frac{-F_{70}\! \left(x , y\right)+F_{70}\! \left(x , 1\right)}{-1+y}\\
F_{85}\! \left(x , y\right) &= F_{21}\! \left(x \right) F_{86}\! \left(x , y\right)\\
F_{86}\! \left(x , y\right) &= -\frac{y \left(-F_{70}\! \left(x , y\right)+F_{70}\! \left(x , 1\right)\right)}{-1+y}\\
F_{87}\! \left(x , y\right) &= F_{88}\! \left(x , y\right)\\
F_{88}\! \left(x , y\right) &= F_{20}\! \left(x , y\right) F_{89}\! \left(x , y\right)\\
F_{89}\! \left(x , y\right) &= F_{195}\! \left(x , y\right)+F_{90}\! \left(x , y\right)\\
F_{90}\! \left(x , y\right) &= F_{91}\! \left(x , y\right)\\
F_{91}\! \left(x , y\right) &= F_{21}\! \left(x \right) F_{92}\! \left(x , y\right)\\
F_{93}\! \left(x , y\right) &= F_{20}\! \left(x , y\right) F_{92}\! \left(x , y\right)\\
F_{93}\! \left(x , y\right) &= F_{94}\! \left(x , y\right)\\
F_{94}\! \left(x , y\right) &= F_{8}\! \left(x , y\right)+F_{95}\! \left(x , y\right)+F_{96}\! \left(x , y\right)\\
F_{95}\! \left(x , y\right) &= F_{20}\! \left(x , y\right) F_{94}\! \left(x , y\right)\\
F_{96}\! \left(x , y\right) &= F_{21}\! \left(x \right) F_{97}\! \left(x , y\right)\\
F_{97}\! \left(x , y\right) &= F_{122}\! \left(x , y\right)+F_{98}\! \left(x , y\right)\\
F_{99}\! \left(x , y\right) &= F_{114}\! \left(x , y\right)+F_{98}\! \left(x , y\right)\\
F_{100}\! \left(x , y\right) &= F_{103}\! \left(x , y\right)+F_{99}\! \left(x , y\right)\\
F_{101}\! \left(x , y\right) &= F_{100}\! \left(x , y\right) F_{20}\! \left(x , y\right)\\
F_{101}\! \left(x , y\right) &= F_{102}\! \left(x , y\right)\\
F_{102}\! \left(x , y\right) &= -\frac{y \left(-F_{8}\! \left(x , y\right)+F_{8}\! \left(x , 1\right)\right)}{-1+y}\\
F_{103}\! \left(x , y\right) &= F_{104}\! \left(x , y\right)\\
F_{104}\! \left(x , y\right) &= F_{105}\! \left(x \right) F_{18}\! \left(x , y\right) F_{21}\! \left(x \right)\\
F_{105}\! \left(x \right) &= F_{106}\! \left(x , 1\right)\\
F_{106}\! \left(x , y\right) &= F_{107}\! \left(x \right)+F_{112}\! \left(x , y\right)\\
F_{107}\! \left(x \right) &= -F_{108}\! \left(x \right)+F_{68}\! \left(x \right)\\
F_{108}\! \left(x \right) &= \frac{F_{109}\! \left(x \right)}{F_{21}\! \left(x \right)}\\
F_{109}\! \left(x \right) &= -F_{37}\! \left(x \right)-F_{5}\! \left(x \right)+F_{110}\! \left(x \right)\\
F_{110}\! \left(x \right) &= -F_{111}\! \left(x \right)+F_{4}\! \left(x \right)\\
F_{111}\! \left(x \right) &= F_{111}\! \left(x \right) x +F_{111} \left(x \right)^{2}-2 F_{111}\! \left(x \right)+2\\
F_{112}\! \left(x , y\right) &= F_{113}\! \left(x , y\right)\\
F_{113}\! \left(x , y\right) &= F_{106}\! \left(x , y\right) F_{111}\! \left(x \right) F_{20}\! \left(x , y\right)\\
F_{114}\! \left(x , y\right) &= F_{115}\! \left(x \right)+F_{120}\! \left(x , y\right)\\
F_{115}\! \left(x \right) &= -F_{118}\! \left(x \right)+F_{116}\! \left(x \right)\\
F_{116}\! \left(x \right) &= \frac{F_{117}\! \left(x \right)}{F_{21}\! \left(x \right)}\\
F_{117}\! \left(x \right) &= F_{7}\! \left(x \right)\\
F_{118}\! \left(x \right) &= F_{119}\! \left(x \right)\\
F_{119}\! \left(x \right) &= F_{105}\! \left(x \right) F_{14}\! \left(x \right) F_{21}\! \left(x \right)\\
F_{120}\! \left(x , y\right) &= F_{121}\! \left(x , y\right)\\
F_{121}\! \left(x , y\right) &= F_{106}\! \left(x , y\right) F_{14}\! \left(x \right) F_{20}\! \left(x , y\right)\\
F_{123}\! \left(x , y\right) &= F_{118}\! \left(x \right)+F_{122}\! \left(x , y\right)\\
F_{123}\! \left(x , y\right) &= F_{124}\! \left(x , y\right)\\
F_{124}\! \left(x , y\right) &= F_{105}\! \left(x \right) F_{125}\! \left(x , y\right) F_{21}\! \left(x \right)\\
F_{126}\! \left(x , y\right) &= F_{125}\! \left(x , y\right) F_{21}\! \left(x \right)\\
F_{126}\! \left(x , y\right) &= F_{127}\! \left(x , y\right)\\
F_{128}\! \left(x , y\right) &= F_{127}\! \left(x , y\right)+F_{183}\! \left(x , y\right)\\
F_{128}\! \left(x , y\right) &= F_{129}\! \left(x , y\right)+F_{194}\! \left(x , y\right)\\
F_{129}\! \left(x , y\right) &= F_{1}\! \left(x \right)+F_{130}\! \left(x , y\right)+F_{191}\! \left(x , y\right)+F_{192}\! \left(x , y\right)+F_{193}\! \left(x , y\right)\\
F_{130}\! \left(x , y\right) &= F_{131}\! \left(x , y\right) F_{21}\! \left(x \right)\\
F_{131}\! \left(x , y\right) &= F_{132}\! \left(x \right)+F_{136}\! \left(x , y\right)\\
F_{132}\! \left(x \right) &= F_{133}\! \left(x , 1\right)\\
F_{133}\! \left(x , y\right) &= F_{134}\! \left(x , y\right)+F_{6}\! \left(x \right)\\
F_{134}\! \left(x , y\right) &= y F_{135}\! \left(x \right)\\
F_{135}\! \left(x \right) &= F_{7}\! \left(x \right)\\
F_{136}\! \left(x , y\right) &= y F_{137}\! \left(x \right)\\
F_{137}\! \left(x \right) &= \frac{F_{138}\! \left(x \right)}{F_{21}\! \left(x \right)}\\
F_{138}\! \left(x \right) &= -F_{173}\! \left(x \right)-F_{174}\! \left(x \right)-F_{175}\! \left(x \right)-F_{37}\! \left(x \right)+F_{139}\! \left(x \right)\\
F_{139}\! \left(x \right) &= F_{140}\! \left(x \right)+F_{7}\! \left(x \right)\\
F_{140}\! \left(x \right) &= -F_{12}\! \left(x \right)+F_{141}\! \left(x \right)\\
F_{141}\! \left(x \right) &= F_{142}\! \left(x \right)\\
F_{142}\! \left(x \right) &= -F_{132}\! \left(x \right)+F_{143}\! \left(x \right)\\
F_{143}\! \left(x \right) &= F_{144}\! \left(x \right)+F_{172}\! \left(x \right)\\
F_{144}\! \left(x \right) &= -F_{167}\! \left(x \right)+F_{145}\! \left(x \right)\\
F_{145}\! \left(x \right) &= F_{146}\! \left(x , 1\right)\\
F_{146}\! \left(x , y\right) &= F_{147}\! \left(x , y\right)+F_{161}\! \left(x , y\right)\\
F_{147}\! \left(x , y\right) &= F_{1}\! \left(x \right)+F_{148}\! \left(x , y\right)+F_{154}\! \left(x , y\right)+F_{158}\! \left(x , y\right)+F_{159}\! \left(x , y\right)\\
F_{148}\! \left(x , y\right) &= F_{149}\! \left(x , y\right) F_{21}\! \left(x \right)\\
F_{149}\! \left(x , y\right) &= F_{150}\! \left(x , y\right)+F_{152}\! \left(x , y\right)\\
F_{150}\! \left(x , y\right) &= -\frac{-F_{151}\! \left(x , y\right) y +F_{151}\! \left(x , 1\right)}{-1+y}\\
F_{151}\! \left(x , y\right) &= F_{4}\! \left(x \right)+F_{8}\! \left(x , y\right)\\
F_{152}\! \left(x , y\right) &= F_{153}\! \left(x , y\right)\\
F_{153}\! \left(x , y\right) &= -\frac{-F_{8}\! \left(x , y\right)+F_{8}\! \left(x , 1\right)}{-1+y}\\
F_{154}\! \left(x , y\right) &= F_{155}\! \left(x , y\right) F_{21}\! \left(x \right)\\
F_{155}\! \left(x , y\right) &= F_{132}\! \left(x \right)+F_{156}\! \left(x , y\right)\\
F_{156}\! \left(x , y\right) &= F_{157}\! \left(x , y\right)\\
F_{157}\! \left(x , y\right) &= y F_{141}\! \left(x \right)\\
F_{158}\! \left(x , y\right) &= F_{146}\! \left(x , y\right) F_{20}\! \left(x , y\right)\\
F_{159}\! \left(x , y\right) &= F_{160}\! \left(x , y\right) F_{21}\! \left(x \right)\\
F_{160}\! \left(x , y\right) &= -\frac{-F_{147}\! \left(x , y\right) y +F_{147}\! \left(x , 1\right)}{-1+y}\\
F_{161}\! \left(x , y\right) &= y F_{162}\! \left(x , y\right)\\
F_{162}\! \left(x , y\right) &= F_{163}\! \left(x , y\right)\\
F_{163}\! \left(x , y\right) &= F_{164}\! \left(x , y\right) F_{21}\! \left(x \right)\\
F_{165}\! \left(x , y\right) &= F_{164}\! \left(x , y\right) F_{20}\! \left(x , y\right)\\
F_{165}\! \left(x , y\right) &= F_{166}\! \left(x , y\right)\\
F_{147}\! \left(x , y\right) &= F_{166}\! \left(x , y\right)+F_{6}\! \left(x \right)\\
F_{167}\! \left(x \right) &= F_{168}\! \left(x , 1\right)\\
F_{169}\! \left(x , y\right) &= -\frac{y \left(F_{168}\! \left(x , 1\right)-F_{168}\! \left(x , y\right)\right)}{-1+y}\\
F_{170}\! \left(x , y\right) &= F_{145}\! \left(x \right)+F_{169}\! \left(x , y\right)\\
F_{170}\! \left(x , y\right) &= -\frac{-y F_{171}\! \left(x , y\right)+F_{171}\! \left(x , 1\right)}{-1+y}\\
F_{171}\! \left(x , y\right) &= F_{147}\! \left(x , y\right)+F_{162}\! \left(x , y\right)\\
F_{172}\! \left(x \right) &= F_{135}\! \left(x \right)\\
F_{173}\! \left(x \right) &= F_{143}\! \left(x \right) F_{21}\! \left(x \right)\\
F_{174}\! \left(x \right) &= F_{21}\! \left(x \right) F_{7}\! \left(x \right)\\
F_{175}\! \left(x \right) &= F_{176}\! \left(x \right) F_{21}\! \left(x \right)\\
F_{176}\! \left(x \right) &= -F_{187}\! \left(x \right)+F_{177}\! \left(x \right)\\
F_{177}\! \left(x \right) &= F_{178}\! \left(x , 1\right)\\
F_{178}\! \left(x , y\right) &= F_{179}\! \left(x , y\right)+F_{185}\! \left(x , y\right)\\
F_{180}\! \left(x , y\right) &= F_{179}\! \left(x , y\right) F_{21}\! \left(x \right)\\
F_{151}\! \left(x , y\right) &= F_{1}\! \left(x \right)+F_{180}\! \left(x , y\right)+F_{181}\! \left(x , y\right)+F_{182}\! \left(x , y\right)\\
F_{181}\! \left(x , y\right) &= F_{133}\! \left(x , y\right) F_{21}\! \left(x \right)\\
F_{182}\! \left(x , y\right) &= F_{183}\! \left(x , y\right) F_{20}\! \left(x , y\right)\\
F_{183}\! \left(x , y\right) &= F_{151}\! \left(x , y\right)+F_{184}\! \left(x , y\right)\\
F_{184}\! \left(x , y\right) &= y F_{11}\! \left(x , y\right)\\
F_{185}\! \left(x , y\right) &= F_{186}\! \left(x , y\right)\\
F_{179}\! \left(x , y\right) &= F_{151}\! \left(x , y\right)+F_{186}\! \left(x , y\right)\\
F_{187}\! \left(x \right) &= \frac{F_{188}\! \left(x \right)}{F_{21}\! \left(x \right)}\\
F_{188}\! \left(x \right) &= -F_{1}\! \left(x \right)-F_{190}\! \left(x \right)-F_{3}\! \left(x \right)+F_{189}\! \left(x \right)\\
F_{189}\! \left(x \right) &= F_{12}\! \left(x \right)+F_{4}\! \left(x \right)\\
F_{190}\! \left(x \right) &= F_{132}\! \left(x \right) F_{21}\! \left(x \right)\\
F_{191}\! \left(x , y\right) &= F_{128}\! \left(x , y\right) F_{20}\! \left(x , y\right)\\
F_{192}\! \left(x , y\right) &= F_{151}\! \left(x , y\right) F_{21}\! \left(x \right)\\
F_{193}\! \left(x , y\right) &= F_{178}\! \left(x , y\right) F_{21}\! \left(x \right)\\
F_{194}\! \left(x , y\right) &= F_{184}\! \left(x , y\right)\\
F_{195}\! \left(x , y\right) &= F_{196}\! \left(x , y\right)\\
F_{196}\! \left(x , y\right) &= F_{14}\! \left(x \right) F_{197}\! \left(x , y\right) F_{21}\! \left(x \right)\\
F_{197}\! \left(x , y\right) &= F_{1}\! \left(x \right)+F_{198}\! \left(x , y\right)+F_{199}\! \left(x , y\right)\\
F_{198}\! \left(x , y\right) &= F_{197}\! \left(x , y\right) F_{20}\! \left(x , y\right)\\
F_{199}\! \left(x , y\right) &= F_{106}\! \left(x , y\right) F_{21}\! \left(x \right)\\
\end{align*}\)