#
# Origin of the problem: F. Seyfert
# [Signal Theory]
# Problem: a) find the number of complex roots (easy)
#          b) find the real roots
#
# Level: Middle
#
#vars [P22, P32, P42, P52, P62, P72, P82, P92, P23, P33, P43, P53, P63, P73, P83, P93, P24, P34, P44, P54, P64, P74, P84, P94, P25, P35, P45, P55, P65, P75, P85, P95, P26, P36, P46, P56, P66, P76, P86, P96, P27, P37, P47, P57, P67, P77, P87, P97, P28, P38, P48, P58, P68, P78, P88, P98, P29, P39, P49, P59, P69, P79, P89, P99]

#list


[P22*P23+P32*P33+P42*P43+P52*P53+P62*P63+P72*P73+P82*P83+P92*P93, P22*P24+P32*P34+P42*P44+P52*P54+P62*P64+P72*P74+P82*P84+P92*P94, P23*P24+P33*P34+P43*P44+P53*P54+P63*P64+P73*P74+P83*P84+P93*P94, P22*P25+P32*P35+P42*P45+P52*P55+P62*P65+P72*P75+P82*P85+P92*P95, P23*P25+P33*P35+P43*P45+P53*P55+P63*P65+P73*P75+P83*P85+P93*P95, P24*P25+P34*P35+P44*P45+P54*P55+P64*P65+P74*P75+P84*P85+P94*P95, P22*P26+P32*P36+P42*P46+P52*P56+P62*P66+P72*P76+P82*P86+P92*P96, P23*P26+P33*P36+P43*P46+P53*P56+P63*P66+P73*P76+P83*P86+P93*P96, P24*P26+P34*P36+P44*P46+P54*P56+P64*P66+P74*P76+P84*P86+P94*P96, P25*P26+P35*P36+P45*P46+P55*P56+P65*P66+P75*P76+P85*P86+P95*P96, P22*P27+P32*P37+P42*P47+P52*P57+P62*P67+P72*P77+P82*P87+P92*P97, P23*P27+P33*P37+P43*P47+P53*P57+P63*P67+P73*P77+P83*P87+P93*P97, P24*P27+P34*P37+P44*P47+P54*P57+P64*P67+P74*P77+P84*P87+P94*P97, P25*P27+P35*P37+P45*P47+P55*P57+P65*P67+P75*P77+P85*P87+P95*P97, P26*P27+P36*P37+P46*P47+P56*P57+P66*P67+P76*P77+P86*P87+P96*P97, P22*P28+P32*P38+P42*P48+P52*P58+P62*P68+P72*P78+P82*P88+P92*P98, P23*P28+P33*P38+P43*P48+P53*P58+P63*P68+P73*P78+P83*P88+P93*P98, P24*P28+P34*P38+P44*P48+P54*P58+P64*P68+P74*P78+P84*P88+P94*P98, P25*P28+P35*P38+P45*P48+P55*P58+P65*P68+P75*P78+P85*P88+P95*P98, P26*P28+P36*P38+P46*P48+P56*P58+P66*P68+P76*P78+P86*P88+P96*P98, P27*P28+P37*P38+P47*P48+P57*P58+P67*P68+P77*P78+P87*P88+P97*P98, P22*P29+P32*P39+P42*P49+P52*P59+P62*P69+P72*P79+P82*P89+P92*P99, P23*P29+P33*P39+P43*P49+P53*P59+P63*P69+P73*P79+P83*P89+P93*P99, P24*P29+P34*P39+P44*P49+P54*P59+P64*P69+P74*P79+P84*P89+P94*P99, P25*P29+P35*P39+P45*P49+P55*P59+P65*P69+P75*P79+P85*P89+P95*P99, P26*P29+P36*P39+P46*P49+P56*P59+P66*P69+P76*P79+P86*P89+P96*P99, P27*P29+P37*P39+P47*P49+P57*P59+P67*P69+P77*P79+P87*P89+P97*P99, P28*P29+P38*P39+P48*P49+P58*P59+P68*P69+P78*P79+P88*P89+P98*P99, P22+P32+P42+P52+P62+P72+P82+P92-1, P23+P33+P43+P53+P63+P73+P83+P93-1, P24+P34+P44+P54+P64+P74+P84+P94-1, P25+P35+P45+P55+P65+P75+P85+P95-1, P26+P36+P46+P56+P66+P76+P86+P96-1, P27+P37+P47+P57+P67+P77+P87+P97-1, P28+P38+P48+P58+P68+P78+P88+P98-1, P29+P39+P49+P59+P69+P79+P89+P99-1, P23, 55*P44*P32+55*P34*P42+60*P34*P22+60*P24*P32+34*P74*P52+34*P54*P72+27*P64*P72+27*P62*P74+54*P74*P82+6*P84*P32+10*P84*P42+54*P84*P72+60*P84*P92+60*P94*P82+6*P34*P82+10*P44*P82+11*P44*P72+11*P74*P42+2*P22*P24+2*P32*P34-25*P52*P54-87*P62*P64-4*P72*P74+2*P82*P84+2*P92*P94+19*P54*P62+19*P64*P52+51*P54*P42+51*P44*P52, P25, 2*P22*P25+2*P32*P35-25*P52*P55-87*P62*P65-4*P72*P75+2*P82*P85+2*P92*P95+54*P85*P72+60*P85*P92+60*P25*P32+60*P35*P22+10*P45*P82+6*P35*P82+19*P65*P52+19*P55*P62+55*P35*P42+34*P72*P55+55*P45*P32+51*P55*P42+51*P45*P52+11*P42*P75+11*P72*P45+34*P52*P75+27*P62*P75+27*P72*P65+6*P85*P32+54*P75*P82+10*P85*P42+60*P95*P82, 2*P23*P25+2*P33*P35-25*P53*P55-87*P63*P65-4*P73*P75+2*P83*P85+2*P93*P95+34*P55*P73+34*P75*P53+55*P35*P43+55*P45*P33+51*P45*P53+51*P55*P43+19*P55*P63+19*P65*P53+6*P85*P33+27*P75*P63+6*P35*P83+60*P35*P23+60*P25*P33+60*P95*P83+60*P85*P93+54*P85*P73+10*P85*P43+11*P75*P43+10*P45*P83+11*P45*P73+27*P65*P73+54*P75*P83, P26, 2*P22*P26+2*P32*P36-25*P52*P56-87*P62*P66-4*P72*P76+2*P82*P86+2*P92*P96+6*P86*P32+54*P76*P82+60*P96*P82+60*P86*P92+54*P86*P72+10*P86*P42+10*P46*P82+6*P36*P82+60*P26*P32+60*P36*P22+55*P36*P42+55*P46*P32+34*P56*P72+34*P76*P52+11*P46*P72+27*P66*P72+11*P76*P42+27*P76*P62+51*P46*P52+51*P56*P42+19*P56*P62+19*P66*P52, -25*P54*P56+2*P34*P36+2*P24*P26-87*P64*P66+2*P84*P86+2*P94*P96-4*P74*P76+60*P26*P34+60*P96*P84+60*P86*P94+54*P86*P74+10*P86*P44+6*P86*P34+54*P76*P84+27*P76*P64+11*P76*P44+27*P66*P74+10*P46*P84+11*P46*P74+6*P36*P84+60*P36*P24+34*P56*P74+34*P76*P54+55*P36*P44+55*P46*P34+51*P46*P54+51*P56*P44+19*P56*P64+19*P66*P54, P27, 2*P22*P27+2*P32*P37-25*P52*P57-87*P62*P67-4*P72*P77+2*P82*P87+2*P92*P97+10*P42*P87+60*P92*P87+60*P82*P97+54*P82*P77+10*P82*P47+6*P82*P37+54*P72*P87+6*P32*P87+11*P72*P47+27*P72*P67+27*P62*P77+11*P42*P77+60*P22*P37+60*P32*P27+55*P32*P47+55*P42*P37+51*P42*P57+51*P52*P47+19*P52*P67+34*P52*P77+19*P62*P57+34*P72*P57, 2*P23*P27+2*P33*P37-25*P53*P57-87*P63*P67-4*P73*P77+2*P83*P87+2*P93*P97+51*P53*P47+19*P53*P67+19*P63*P57+60*P23*P37+60*P33*P27+6*P33*P87+10*P43*P87+6*P83*P37+54*P73*P87+60*P93*P87+60*P83*P97+54*P83*P77+10*P83*P47+27*P77*P63+27*P67*P73+11*P47*P73+34*P57*P73+11*P77*P43+34*P77*P53+55*P33*P47+55*P43*P37+51*P43*P57, 2*P24*P27+2*P34*P37-25*P54*P57-87*P64*P67-4*P74*P77+2*P84*P87+2*P94*P97+55*P37*P44+55*P47*P34+51*P47*P54+51*P57*P44+19*P57*P64+34*P57*P74+19*P67*P54+34*P77*P54+6*P87*P34+54*P77*P84+27*P77*P64+11*P77*P44+27*P67*P74+10*P47*P84+11*P47*P74+6*P37*P84+60*P37*P24+60*P27*P34+60*P97*P84+60*P87*P94+54*P87*P74+10*P87*P44, 2*P25*P27+2*P35*P37-25*P55*P57-87*P65*P67-4*P75*P77+2*P85*P87+2*P95*P97+51*P47*P55+55*P47*P35+6*P37*P85+55*P37*P45+60*P37*P25+60*P27*P35+54*P77*P85+27*P77*P65+34*P77*P55+11*P77*P45+27*P67*P75+19*P67*P55+34*P57*P75+19*P57*P65+51*P57*P45+10*P47*P85+11*P47*P75+6*P87*P35+10*P87*P45+60*P97*P85+60*P87*P95+54*P87*P75, P28, 2*P22*P28+2*P32*P38-25*P52*P58-87*P62*P68-4*P72*P78+2*P82*P88+2*P92*P98+54*P82*P78+10*P82*P48+6*P82*P38+54*P72*P88+27*P72*P68+34*P72*P58+11*P72*P48+27*P62*P78+19*P62*P58+34*P52*P78+19*P52*P68+51*P52*P48+10*P42*P88+11*P42*P78+51*P42*P58+55*P42*P38+6*P32*P88+55*P32*P48+60*P32*P28+60*P82*P98+60*P92*P88+60*P22*P38, 2*P23*P28+2*P33*P38-25*P53*P58-87*P63*P68-4*P73*P78+2*P83*P88+2*P93*P98+11*P43*P78+51*P43*P58+55*P43*P38+6*P33*P88+55*P33*P48+60*P33*P28+60*P23*P38+10*P43*P88+51*P53*P48+34*P53*P78+19*P53*P68+27*P63*P78+19*P63*P58+60*P83*P98+54*P83*P78+10*P83*P48+6*P83*P38+54*P73*P88+34*P73*P58+11*P73*P48+60*P93*P88+27*P73*P68, 2*P24*P28+2*P34*P38-25*P54*P58-87*P64*P68-4*P74*P78+2*P84*P88+2*P94*P98+55*P48*P34+6*P38*P84+55*P38*P44+60*P38*P24+60*P28*P34+60*P98*P84+60*P88*P94+54*P88*P74+10*P88*P44+6*P88*P34+54*P78*P84+27*P78*P64+34*P78*P54+11*P78*P44+27*P68*P74+19*P68*P54+34*P58*P74+19*P58*P64+51*P58*P44+10*P48*P84+11*P48*P74+51*P48*P54, 2*P86*P88-4*P76*P78-87*P66*P68-25*P56*P58+2*P36*P38+2*P26*P28+2*P96*P98+60*P28*P36+27*P68*P76+19*P68*P56+34*P58*P76+19*P58*P66+51*P58*P46+10*P48*P86+11*P48*P76+51*P48*P56+55*P48*P36+6*P38*P86+55*P38*P46+60*P38*P26+34*P78*P56+11*P78*P46+54*P78*P86+27*P78*P66+54*P88*P76+10*P88*P46+6*P88*P36+60*P88*P96+60*P98*P86, P29, 2*P22*P29+2*P32*P39-25*P52*P59-87*P62*P69-4*P72*P79+2*P82*P89+2*P92*P99+10*P49*P82+11*P49*P72+51*P49*P52+55*P49*P32+6*P39*P82+55*P39*P42+60*P39*P22+60*P29*P32+51*P59*P42+19*P69*P52+34*P59*P72+19*P59*P62+60*P99*P82+60*P89*P92+54*P89*P72+10*P89*P42+6*P89*P32+54*P79*P82+27*P79*P62+34*P79*P52+11*P79*P42+27*P69*P72, 2*P23*P29+2*P33*P39-25*P53*P59-87*P63*P69-4*P73*P79+2*P83*P89+2*P93*P99+60*P29*P33+60*P39*P23+55*P39*P43+6*P39*P83+55*P49*P33+34*P79*P53+11*P79*P43+27*P69*P73+19*P69*P53+34*P59*P73+19*P59*P63+51*P59*P43+10*P49*P83+11*P49*P73+51*P49*P53+54*P79*P83+27*P79*P63+10*P89*P43+6*P89*P33+60*P99*P83+60*P89*P93+54*P89*P73, 2*P24*P29+2*P34*P39-25*P54*P59-87*P64*P69-4*P74*P79+2*P84*P89+2*P94*P99+60*P29*P34+60*P39*P24+11*P49*P74+51*P49*P54+55*P49*P34+6*P39*P84+55*P39*P44+51*P59*P44+10*P49*P84+27*P69*P74+19*P69*P54+34*P59*P74+19*P59*P64+11*P79*P44+34*P79*P54+27*P79*P64+6*P89*P34+54*P79*P84+60*P99*P84+60*P89*P94+54*P89*P74+10*P89*P44, 2*P25*P29+2*P35*P39-25*P55*P59-87*P65*P69-4*P75*P79+2*P85*P89+2*P95*P99+55*P39*P45+60*P39*P25+60*P29*P35+34*P79*P55+11*P79*P45+27*P69*P75+19*P69*P55+34*P59*P75+19*P59*P65+51*P59*P45+10*P49*P85+11*P49*P75+51*P49*P55+55*P49*P35+6*P39*P85+54*P79*P85+27*P79*P65+60*P99*P85+60*P89*P95+54*P89*P75+10*P89*P45+6*P89*P35, 2*P26*P29+2*P36*P39-25*P56*P59-87*P66*P69-4*P76*P79+2*P86*P89+2*P96*P99+11*P46*P79+51*P46*P59+55*P46*P39+6*P36*P89+55*P36*P49+60*P36*P29+60*P26*P39+11*P76*P49+27*P66*P79+19*P66*P59+34*P56*P79+19*P56*P69+51*P56*P49+10*P46*P89+27*P76*P69+34*P76*P59+60*P96*P89+60*P86*P99+54*P86*P79+10*P86*P49+6*P86*P39+54*P76*P89, 2*P27*P29+2*P37*P39-25*P57*P59-87*P67*P69-4*P77*P79+2*P87*P89+2*P97*P99+19*P57*P69+51*P57*P49+10*P47*P89+11*P47*P79+51*P47*P59+55*P47*P39+6*P37*P89+55*P37*P49+60*P37*P29+60*P27*P39+34*P57*P79+19*P67*P59+27*P67*P79+27*P77*P69+34*P77*P59+11*P77*P49+60*P97*P89+60*P87*P99+54*P87*P79+10*P87*P49+6*P87*P39+54*P77*P89, P92, P93, P94, P95, P96, P98, 3604*P22*P25+6665*P32*P35+4743*P52*P55+5847*P42*P45+8659*P62*P65+4938*P72*P75+6656*P82*P85+11000*P92*P95+2*P85*P72+240*P85*P92+240*P25*P32+240*P35*P22+944*P45*P82+574*P35*P82-1210*P65*P52-1210*P55*P62+170*P35*P42+88*P72*P55+170*P45*P32-901*P55*P42-901*P45*P52+2230*P42*P75+2230*P72*P45+88*P52*P75-1811*P62*P75-1811*P72*P65+574*P85*P32+2*P75*P82+944*P85*P42+240*P95*P82+3300*P22*P45+2805*P32*P55+1266*P42*P65+2805*P52*P35+1266*P62*P45+3300*P42*P25+929*P72*P35+929*P32*P75+600*P42*P95+360*P32*P95+360*P22*P85+1458*P62*P85+2346*P52*P85+3240*P92*P75+600*P92*P45+360*P92*P35+1458*P82*P65+2346*P82*P55+360*P82*P25+3240*P72*P95, 3604*P22*P27+6665*P32*P37+4743*P52*P57+5847*P42*P47+8659*P62*P67+4938*P72*P77+6656*P82*P87+11000*P92*P97+1266*P62*P47+2805*P52*P37+1266*P42*P67+3300*P42*P27+2805*P32*P57+3300*P22*P47+2346*P52*P87+1458*P62*P87+3240*P72*P97+360*P82*P27+2346*P82*P57+1458*P82*P67+360*P92*P37+600*P92*P47+3240*P92*P77+600*P42*P97+929*P32*P77+929*P72*P37+360*P22*P87+360*P32*P97+944*P42*P87+240*P92*P87+240*P82*P97+2*P82*P77+944*P82*P47+574*P82*P37+2*P72*P87+574*P32*P87+2230*P72*P47-1811*P72*P67-1811*P62*P77+2230*P42*P77+240*P22*P37+240*P32*P27+170*P32*P47+170*P42*P37-901*P42*P57-901*P52*P47-1210*P52*P67+88*P52*P77-1210*P62*P57+88*P72*P57, 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P47*P79-P77*P49, P47*P89-P87*P49, P57*P69-P67*P59, P57*P79-P77*P59, P57*P89-P87*P59, P67*P79-P77*P69, P67*P89-P87*P69, P77*P89-P87*P79]