# Origin of the problem: F. Seyfert # Problem: a) find the number of complex roots # b) find the real roots # # [Signal Theory] # Level: Difficult # #vars[P22, P32, P42, P52, P62, P72, P82, P92, P102, P23, P33, P43, P53, P63, P73, P83, P93, P103, P24, P34, P44, P54, P64, P74, P84, P94, P104, P25, P35, P45, P55, P65, P75, P85, P95, P105, P26, P36, P46, P56, P66, P76, P86, P96, P106, P27, P37, P47, P57, P67, P77, P87, P97, P107, P28, P38, P48, P58, P68, P78, P88, P98, P108, P29, P39, P49, P59, P69, P79, P89, P99, P109, P210, P310, P410, P510, P610, P710, P810, P910, P1010] #list[ P22*P23+P32*P33+P42*P43+P52*P53+P62*P63+P72*P73+P82*P83+P92*P93+P102*P103, P22*P24+P32*P34+P42*P44+P52*P54+P62*P64+P72*P74+P82*P84+P92*P94+P102*P104, P23*P24+P33*P34+P43*P44+P53*P54+P63*P64+P73*P74+P83*P84+P93*P94+P103*P104, P22*P25+P32*P35+P42*P45+P52*P55+P62*P65+P72*P75+P82*P85+P92*P95+P102*P105, P23*P25+P33*P35+P43*P45+P53*P55+P63*P65+P73*P75+P83*P85+P93*P95+P103*P105, P24*P25+P34*P35+P44*P45+P54*P55+P64*P65+P74*P75+P84*P85+P94*P95+P104*P105, P22*P26+P32*P36+P42*P46+P52*P56+P62*P66+P72*P76+P82*P86+P92*P96+P102*P106, P23*P26+P33*P36+P43*P46+P53*P56+P63*P66+P73*P76+P83*P86+P93*P96+P103*P106, P24*P26+P34*P36+P44*P46+P54*P56+P64*P66+P74*P76+P84*P86+P94*P96+P104*P106, P25*P26+P35*P36+P45*P46+P55*P56+P65*P66+P75*P76+P85*P86+P95*P96+P105*P106, P22*P27+P32*P37+P42*P47+P52*P57+P62*P67+P72*P77+P82*P87+P92*P97+P102*P107, P23*P27+P33*P37+P43*P47+P53*P57+P63*P67+P73*P77+P83*P87+P93*P97+P103*P107, P24*P27+P34*P37+P44*P47+P54*P57+P64*P67+P74*P77+P84*P87+P94*P97+P104*P107, P25*P27+P35*P37+P45*P47+P55*P57+P65*P67+P75*P77+P85*P87+P95*P97+P105*P107, P26*P27+P36*P37+P46*P47+P56*P57+P66*P67+P76*P77+P86*P87+P96*P97+P106*P107, P22*P28+P32*P38+P42*P48+P52*P58+P62*P68+P72*P78+P82*P88+P92*P98+P102*P108, P23*P28+P33*P38+P43*P48+P53*P58+P63*P68+P73*P78+P83*P88+P93*P98+P103*P108, P24*P28+P34*P38+P44*P48+P54*P58+P64*P68+P74*P78+P84*P88+P94*P98+P104*P108, P25*P28+P35*P38+P45*P48+P55*P58+P65*P68+P75*P78+P85*P88+P95*P98+P105*P108, P26*P28+P36*P38+P46*P48+P56*P58+P66*P68+P76*P78+P86*P88+P96*P98+P106*P108, P27*P28+P37*P38+P47*P48+P57*P58+P67*P68+P77*P78+P87*P88+P97*P98+P107*P108, P22*P29+P32*P39+P42*P49+P52*P59+P62*P69+P72*P79+P82*P89+P92*P99+P102*P109, P23*P29+P33*P39+P43*P49+P53*P59+P63*P69+P73*P79+P83*P89+P93*P99+P103*P109, P24*P29+P34*P39+P44*P49+P54*P59+P64*P69+P74*P79+P84*P89+P94*P99+P104*P109, P25*P29+P35*P39+P45*P49+P55*P59+P65*P69+P75*P79+P85*P89+P95*P99+P105*P109, P26*P29+P36*P39+P46*P49+P56*P59+P66*P69+P76*P79+P86*P89+P96*P99+P106*P109, P27*P29+P37*P39+P47*P49+P57*P59+P67*P69+P77*P79+P87*P89+P97*P99+P107*P109, P28*P29+P38*P39+P48*P49+P58*P59+P68*P69+P78*P79+P88*P89+P98*P99+P108*P109, P22*P210+P32*P310+P42*P410+P52*P510+P62*P610+P72*P710+P82*P810+P92*P910+P102*P1010, P23*P210+P33*P310+P43*P410+P53*P510+P63*P610+P73*P710+P83*P810+P93*P910+P103*P1010, P24*P210+P34*P310+P44*P410+P54*P510+P64*P610+P74*P710+P84*P810+P94*P910+P104*P1010, P25*P210+P35*P310+P45*P410+P55*P510+P65*P610+P75*P710+P85*P810+P95*P910+P105*P1010, P26*P210+P36*P310+P46*P410+P56*P510+P66*P610+P76*P710+P86*P810+P96*P910+P106*P1010, P27*P210+P37*P310+P47*P410+P57*P510+P67*P610+P77*P710+P87*P810+P97*P910+P107*P1010, P28*P210+P38*P310+P48*P410+P58*P510+P68*P610+P78*P710+P88*P810+P98*P910+P108*P1010, P29*P210+P39*P310+P49*P410+P59*P510+P69*P610+P79*P710+P89*P810+P99*P910+P109*P1010, P22+P32+P42+P52+P62+P72+P82+P92+P102-1, P23+P33+P43+P53+P63+P73+P83+P93+P103-1, P24+P34+P44+P54+P64+P74+P84+P94+P104-1, P25+P35+P45+P55+P65+P75+P85+P95+P105-1, P26+P36+P46+P56+P66+P76+P86+P96+P106-1, P27+P37+P47+P57+P67+P77+P87+P97+P107-1, P28+P38+P48+P58+P68+P78+P88+P98+P108-1, P29+P39+P49+P59+P69+P79+P89+P99+P109-1, P210+P310+P410+P510+P610+P710+P810+P910+P1010-1, 10*P23+28*P43, 8*P22*P24+79*P32*P34+6*P42*P44+19*P52*P54+46*P62*P64+22*P72*P74+47*P24*P32+47*P34*P22+38*P34*P42+22*P34*P62+38*P44*P32+2*P44*P52+2*P54*P42+38*P54*P62+22*P64*P32+38*P64*P52+21*P64*P72+21*P74*P62+39*P82*P84+35*P92*P94+75*P102*P104+25*P54*P82+55*P74*P82+10*P74*P102+25*P84*P52+55*P84*P72+94*P84*P92+94*P94*P82+76*P94*P102+10*P104*P72+76*P104*P92, 10*P25+28*P45, 8*P22*P25+79*P32*P35+6*P42*P45+19*P52*P55+46*P62*P65+22*P72*P75+47*P22*P35+47*P32*P25+38*P32*P45+22*P32*P65+38*P42*P35+2*P42*P55+2*P52*P45+38*P52*P65+22*P62*P35+38*P62*P55+21*P62*P75+21*P72*P65+39*P82*P85+35*P92*P95+75*P102*P105+25*P52*P85+55*P72*P85+10*P72*P105+25*P82*P55+55*P82*P75+94*P82*P95+94*P92*P85+76*P92*P105+10*P102*P75+76*P102*P95, 25*P83*P55+55*P83*P75+94*P83*P95+94*P93*P85+76*P93*P105+10*P103*P75+76*P103*P95+25*P53*P85+55*P73*P85+10*P73*P105+8*P23*P25+79*P33*P35+6*P43*P45+19*P53*P55+46*P63*P65+22*P73*P75+21*P63*P75+21*P73*P65+47*P23*P35+47*P33*P25+38*P33*P45+22*P33*P65+38*P43*P35+2*P43*P55+2*P53*P45+38*P53*P65+38*P63*P55+22*P63*P35+39*P83*P85+35*P93*P95+75*P103*P105, 10*P26+28*P46, 8*P22*P26+79*P32*P36+6*P42*P46+19*P52*P56+46*P62*P66+22*P72*P76+25*P52*P86+22*P32*P66+38*P32*P46+21*P62*P76+2*P52*P46+47*P32*P26+22*P62*P36+47*P22*P36+38*P42*P36+21*P72*P66+2*P42*P56+38*P62*P56+38*P52*P66+55*P72*P86+10*P72*P106+25*P82*P56+55*P82*P76+94*P82*P96+94*P92*P86+76*P92*P106+10*P102*P76+76*P102*P96+39*P82*P86+35*P92*P96+75*P102*P106, 47*P26*P34+47*P36*P24+38*P36*P44+22*P36*P64+38*P46*P34+2*P46*P54+2*P56*P44+38*P56*P64+22*P66*P34+38*P66*P54+21*P66*P74+21*P76*P64+8*P24*P26+79*P34*P36+6*P44*P46+19*P54*P56+46*P64*P66+22*P74*P76+25*P56*P84+55*P76*P84+10*P76*P104+25*P86*P54+55*P86*P74+94*P86*P94+94*P96*P84+76*P96*P104+10*P106*P74+76*P106*P94+39*P84*P86+35*P94*P96+75*P104*P106, 10*P27+28*P47, 8*P22*P27+79*P32*P37+6*P42*P47+19*P52*P57+46*P62*P67+22*P72*P77+47*P22*P37+47*P32*P27+38*P32*P47+22*P32*P67+38*P42*P37+2*P42*P57+38*P52*P67+22*P62*P37+38*P62*P57+21*P72*P67+2*P52*P47+21*P62*P77+39*P82*P87+35*P92*P97+75*P102*P107+55*P72*P87+10*P72*P107+25*P82*P57+55*P82*P77+94*P82*P97+94*P92*P87+76*P92*P107+25*P52*P87+10*P102*P77+76*P102*P97, 8*P23*P27+79*P33*P37+6*P43*P47+19*P53*P57+46*P63*P67+22*P73*P77+21*P63*P77+21*P73*P67+47*P23*P37+47*P33*P27+38*P33*P47+22*P33*P67+38*P43*P37+2*P43*P57+2*P53*P47+38*P53*P67+22*P63*P37+38*P63*P57+39*P83*P87+35*P93*P97+75*P103*P107+25*P53*P87+10*P103*P77+76*P103*P97+55*P73*P87+10*P73*P107+25*P83*P57+55*P83*P77+94*P83*P97+94*P93*P87+76*P93*P107, 47*P27*P34+47*P37*P24+38*P37*P44+22*P37*P64+38*P47*P34+2*P47*P54+2*P57*P44+38*P57*P64+22*P67*P34+38*P67*P54+21*P67*P74+21*P77*P64+8*P24*P27+79*P34*P37+6*P44*P47+19*P54*P57+46*P64*P67+22*P74*P77+25*P57*P84+55*P77*P84+10*P77*P104+25*P87*P54+55*P87*P74+94*P87*P94+94*P97*P84+76*P97*P104+10*P107*P74+76*P107*P94+39*P84*P87+35*P94*P97+75*P104*P107, 55*P75*P87+10*P75*P107+25*P85*P57+55*P85*P77+94*P85*P97+94*P95*P87+76*P95*P107+10*P105*P77+76*P105*P97+38*P65*P57+21*P65*P77+21*P75*P67+22*P65*P37+47*P25*P37+47*P35*P27+38*P35*P47+22*P35*P67+38*P45*P37+2*P45*P57+2*P55*P47+38*P55*P67+8*P25*P27+79*P35*P37+6*P45*P47+19*P55*P57+46*P65*P67+22*P75*P77+25*P55*P87+39*P85*P87+35*P95*P97+75*P105*P107, 10*P28+28*P48, 47*P22*P38+47*P32*P28+38*P32*P48+38*P42*P38+2*P42*P58+2*P52*P48+38*P52*P68+25*P52*P88+22*P62*P38+38*P62*P58+21*P62*P78+21*P72*P68+55*P72*P88+10*P72*P108+25*P82*P58+55*P82*P78+94*P82*P98+22*P32*P68+94*P92*P88+76*P92*P108+10*P102*P78+76*P102*P98+8*P22*P28+79*P32*P38+6*P42*P48+19*P52*P58+46*P62*P68+22*P72*P78+39*P82*P88+35*P92*P98+75*P102*P108, 47*P23*P38+47*P33*P28+38*P33*P48+22*P33*P68+38*P43*P38+2*P43*P58+2*P53*P48+38*P53*P68+25*P53*P88+22*P63*P38+38*P63*P58+21*P63*P78+21*P73*P68+55*P73*P88+10*P73*P108+25*P83*P58+55*P83*P78+94*P83*P98+94*P93*P88+76*P93*P108+10*P103*P78+76*P103*P98+8*P23*P28+79*P33*P38+6*P43*P48+19*P53*P58+46*P63*P68+22*P73*P78+39*P83*P88+35*P93*P98+75*P103*P108, 47*P24*P38+38*P34*P48+22*P34*P68+2*P54*P48+38*P44*P38+2*P44*P58+38*P54*P68+25*P54*P88+22*P64*P38+38*P64*P58+21*P64*P78+21*P74*P68+10*P74*P108+25*P84*P58+55*P84*P78+47*P34*P28+8*P24*P28+79*P34*P38+6*P44*P48+19*P54*P58+46*P64*P68+22*P74*P78+39*P84*P88+35*P94*P98+75*P104*P108+94*P84*P98+94*P94*P88+76*P94*P108+10*P104*P78+76*P104*P98+55*P74*P88, 8*P26*P28+79*P36*P38+6*P46*P48+19*P56*P58+46*P66*P68+22*P76*P78+39*P86*P88+47*P28*P36+47*P38*P26+38*P38*P46+22*P38*P66+38*P48*P36+2*P48*P56+2*P58*P46+38*P58*P66+25*P58*P86+22*P68*P36+21*P68*P76+21*P78*P66+55*P78*P86+10*P78*P106+25*P88*P56+55*P88*P76+94*P88*P96+94*P98*P86+76*P98*P106+10*P108*P76+76*P108*P96+38*P68*P56+35*P96*P98+75*P106*P108, 10*P29+28*P49, 47*P29*P32+47*P39*P22+38*P39*P42+38*P49*P32+2*P49*P52+2*P59*P42+38*P59*P62+25*P59*P82+22*P69*P32+38*P69*P52+21*P69*P72+21*P79*P62+55*P79*P82+10*P79*P102+25*P89*P52+55*P89*P72+94*P89*P92+22*P39*P62+94*P99*P82+76*P99*P102+76*P109*P92+10*P109*P72+8*P22*P29+79*P32*P39+6*P42*P49+19*P52*P59+46*P62*P69+22*P72*P79+39*P82*P89+35*P92*P99+75*P102*P109, 47*P29*P33+47*P39*P23+38*P39*P43+22*P39*P63+38*P49*P33+22*P69*P33+21*P69*P73+21*P79*P63+55*P79*P83+10*P79*P103+25*P89*P53+55*P89*P73+94*P89*P93+94*P99*P83+76*P99*P103+38*P69*P53+2*P59*P43+38*P59*P63+25*P59*P83+2*P49*P53+8*P23*P29+79*P33*P39+10*P109*P73+76*P109*P93+6*P43*P49+19*P53*P59+46*P63*P69+22*P73*P79+39*P83*P89+35*P93*P99+75*P103*P109, 47*P29*P34+38*P39*P44+22*P39*P64+38*P49*P34+2*P59*P44+38*P59*P64+25*P59*P84+22*P69*P34+38*P69*P54+21*P69*P74+21*P79*P64+55*P79*P84+10*P79*P104+25*P89*P54+2*P49*P54+47*P39*P24+55*P89*P74+94*P89*P94+94*P99*P84+76*P99*P104+76*P109*P94+10*P109*P74+8*P24*P29+79*P34*P39+6*P44*P49+19*P54*P59+46*P64*P69+22*P74*P79+39*P84*P89+35*P94*P99+75*P104*P109, 47*P29*P35+47*P39*P25+38*P39*P45+22*P39*P65+38*P49*P35+2*P49*P55+38*P59*P65+2*P59*P45+25*P59*P85+22*P69*P35+21*P69*P75+21*P79*P65+55*P79*P85+10*P79*P105+25*P89*P55+55*P89*P75+94*P89*P95+94*P99*P85+76*P99*P105+10*P109*P75+76*P109*P95+38*P69*P55+8*P25*P29+79*P35*P39+6*P45*P49+19*P55*P59+46*P65*P69+22*P75*P79+39*P85*P89+35*P95*P99+75*P105*P109, 47*P26*P39+47*P36*P29+38*P36*P49+22*P36*P69+38*P46*P39+2*P46*P59+2*P56*P49+38*P56*P69+25*P56*P89+22*P66*P39+38*P66*P59+21*P66*P79+55*P76*P89+10*P76*P109+25*P86*P59+55*P86*P79+94*P86*P99+94*P96*P89+76*P96*P109+10*P106*P79+76*P106*P99+21*P76*P69+8*P26*P29+79*P36*P39+6*P46*P49+19*P56*P59+46*P66*P69+22*P76*P79+39*P86*P89+35*P96*P99+75*P106*P109, 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