~v300 200 y#hYWm]hV\b\Dlg[D\Xj yzw$PSSjTgMNRWWRZ]YdTQ ~w156 5 411 795 0 602 0 0 ~f? 14 12 10 ? 3 1 1 0 ? ? ? "Arial" ? ? ? 1 ? 0 1 "Times" 12 ? ? 5 0 c n 106 1 0 0 k 468 i"?n page ?p?a" ? 1 26177 26178 26115 26178 1 1 1 1 0 0 8405120 0 -1 0 0 -1 -1 -1 -1 -1 0 1 1 0 2 0 ? ? ? ? ? ? ? ? ~Q ]|Expr|[#b @`bb#_b#_b#_})%# b'4" *|: ;bP8&c0!*Incomplete Gamma| | Series}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p1 0 ~V?f0 (Gamma)~p0 1 ~V?f35 ('G)~p0 1 ~V?f0 ('g)~p0 1 ~V?f0 (f)~p0 1 ~Q ]|Expr|[#b @`bb#_b#_b#_})!# b$L" *|: ;bP8&c0!*Trigonometry| |}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p1 1 ~V?c1 ('p)~p0 2 ~V?f256 (sin)~p0 2 ~V?f257 (cos)~p0 2 ~V?f258 (tan)~p0 2 ~V?f261 (sec)~p0 2 ~V?f260 (csc)~p0 2 ~V?f262 (cot)~p0 2 ~V?f272 (arcsin)~p0 2 ~V?f273 (arccos)~p0 2 ~V?f274 (arctan)~p0 2 ~Q ]|Expr|[#b @`bb#_b#_b#_})!# b$L" *|: ;bP8&c0!*Hyperbolic| |}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p1 1 ~V?f293 (sech)~p0 2 ~V?f288 (sinh)~p0 2 ~V?f289 (cosh)~p0 2 ~V?f290 (tanh)~p0 2 ~Q ]|Expr|[#b @`bb#_b#_b#_})%# b$L" *|: ;bP8&c0!*Logarithms ,F Powers| |}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p1 1 ~V?f32 (log)~p0 2 ~V?f307 (ln)~p0 2 ~V?f291 (exp)~p0 2 ~V?c2 (e)~p0 2 ~Q ]|Expr|[#b @`bb#_b#_b#_})## b$L" *|: ;bP8&c0!*Standard Rules| |}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p1 1 ~Q ]|Expr|[#b @`bb#_b#_b#_})%# b$L" *|: ;bP8&c0!*Logarithms ,F Powers| |}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p1 2 ~Ht(?x^(-?y)):(1/?x^?y)~p0 3 ~Hs(exp(?z)):(e^?z)~p0 3 ~Hs(e^(ln(?x))):(?x)~p0 3 ~Hs(10^(log(?x))):(?x)~p0 3 ~Hs(?y^(log_?y(?x))):(?x)~p0 3 ~Hs(ln(e^?x)):(?x)~p0 3 ~Hs(log(10^?x)):(?x)~p0 3 ~Hs(log_?y(?y^?x)):(?x)~p0 3 ~He(ln(?u*?v)):(ln(?u)+ln(?v))~p0 3 ~He(log(?u*?v)):(log(?u)+log(?v))~p0 3 ~He(log_?y(?u*?v)):(log_?y(?u)+log_?y(?v))~p0 3 ~He(ln(?u/?v)):(ln(?u)-ln(?v))~p0 3 ~He(log(?u/?v)):(log(?u)-log(?v))~p0 3 ~He(log_?y(?u/?v)):(log_?y(?u)-log_?y(?v))~p0 3 ~He(ln(?u^?v)):(?v*ln(?u))~p0 3 ~He(log(?u^?v)):(?v*log(?u))~p0 3 ~He(log_?y(?u^?v)):(?v*log_?y(?u))~p0 3 ~He(ln(sqrt(?u))):(1/2*ln(?u))~p0 3 ~He(log(sqrt(?u))):(1/2*log(?u))~p0 3 ~He(log_?y(sqrt(?u))):(1/2*log_?y(?u))~p0 3 ~Q ]|Expr|[#b @`bb#_b#_b#_})!# b$L" *|: ;bP8&c0!*Trigonometry| |}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p1 2 ~Q ]|Expr|[#b @`bb#_b#_b#_})+# b$L" *|: ;bP8&c0!*Simplify ,M negation| | and common zeros}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p1 3 ~Hs(sin(-?x)):(-sin(?x))~p0 4 ~Hs(cos(-?x)):(cos(?x))~p0 4 ~Hs(tan(-?x)):(-tan(?x))~p0 4 ~Hs(sin('p)):(0)~p0 4 ~Hs(sin(?n*'p)):(0)~p0 4 ~Hs(cos(1/2*'p)):(0)~p0 4 ~Hs(cos(?n/2*'p)):(0)~p0 4 ~Q ]|Expr|[#b @`bb#_b#_b#_})'# b$L" *|: ;bP8&c0!*Transform to basic| | types}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p1 3 ~Ht(tan(?x)):((sin(?x))/(cos(?x)))~p0 4 ~Ht(csc(?x)):(1/(sin(?x)))~p0 4 ~Ht(sin(?x)):(1/(csc(?x)))~p0 4 ~Ht(sec(?x)):(1/(cos(?x)))~p0 4 ~Ht(cos(?x)):(1/(sec(?x)))~p0 4 ~Ht(cot(?x)):((cos(?x))/(sin(?x)))~p0 4 ~Q ]|Expr|[#b @`bb#_b#_b#_})## b$L" *|: ;bP8&c0!*Trig Addition| |}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p1 3 ~Ht(cos(?x+?y)):(cos(?x)*cos(?y)-sin(?x)*sin(?y))~p0 4 ~Ht(sin(?x+?y)):(cos(?x)*sin(?y)+sin(?x)*cos(?y))~p0 4 ~Ht(cos(2*?x)):(2*(cos(?x))^2-1)~p0 4 ~Ht(sin(2*?x)):(2*cos(?x)*sin(?x))~p0 4 ~Ht(sin(?n*?x)):(cos((?n-1)*?x)*sin(?x)+cos(?x)*~ sin((?n-1)*?x))~p0 4 ~Ht(cos(?n*?x)):(cos(?x)*cos((?n-1)*?x)-sin(?x)*~ sin((?n-1)*?x))~p0 4 ~Q ]|Expr|[#b @`bb#_b#_b#_})/# b$L" *|: ;bP8&c0!*Transform ,M into| | another flavor of trig function}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p1 3 ~Ht((sin(?x))^2):(1-(cos(?x))^2)~p0 4 ~Ht((cos(?x))^2):(1-(sin(?x))^2)~p0 4 ~Ht((tan(?x))^2):((sec(?x))^2-1)~p0 4 ~Ht((sec(?x))^2):((tan(?x))^2+1)~p0 4 ~Ht((csc(?x))^2):((cot(?x))^2+1)~p0 4 ~Ht((cot(?x))^2):((csc(?x))^2-1)~p0 4 ~Hs((sin(?x))^2+(cos(?x))^2):(1)~p0 4 ~Q ]|Expr|[#b @`bb#_b#_b#_})b @# b%4" *|: ;bP8&c0!*substituting | |z,]tan,Hx,O2,I into a rational function in sin,Hx,I and cos,H| |x,I}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p1 3 ~Hs(cos(2*arctan(?z))):((1-?z^2)/(1+?z^2))~p0 4 ~Hs(sin(2*arctan(?z))):(2*?z/(1+?z^2))~p0 4 ~Q ]|Expr|[#b @`bb#_b#_b#_})## b$L" *|: ;bP8&c0!*Other rules| |}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p1 3 ~Ht((cos(?x))^2):(1/2*(cos(2*?x)+1))~p0 4 ~Ht((sin(?x))^2):(1/2*(-cos(2*?x)+1))~p0 4 ~Ht(cos(?x)*sin(?x)):(1/2*sin(2*?x))~p0 4 ~Hs(sin(arccos(?x))):(sqrt(-?x^2+1))~p0 4 ~Hs(cos(arcsin(?x))):(sqrt(-?x^2+1))~p0 4 ~Q ]|Expr|[#b @`bb#_b#_b#_})!# b!T" *|: ;bP8&c0!*Hyperbolic| |}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p1 2 ~Q ]|Expr|[#b @`bb#_b#_b#_})+# b$L" *|: ;bP8&c0!*Simplify ,M negation| | and common zeros}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p1 3 ~Hs(sinh(-?x)):(-sinh(?x))~p0 4 ~Hs(cosh(-?x)):(cosh(?x))~p0 4 ~Hs(tanh(-?x)):(-tanh(?x))~p0 4 ~Q ]|Expr|[#b @`bb#_b#_b#_})'# b$L" *|: ;bP8&c0!*Transform into | |other types}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p1 3 ~Ht((sinh(?x))^2):((cosh(?x))^2-1)~p0 4 ~Ht((cosh(?x))^2):(1+(sinh(?x))^2)~p0 4 ~Ht((tanh(?x))^2):(1-(sech(?x))^2)~p0 4 ~Ht(sinh(?x)):((e^?x-e^(-?x))/2)~p0 4 ~Ht(cosh(?x)):((e^?x+e^(-?x))/2)~p0 4 ~Ht(tanh(?x)):((e^?x-e^(-?x))/(e^?x+e^(-?x)))~p0 4 ~Ht(tanh(?x)):((sinh(?x))/(cosh(?x)))~p0 4 ~Hs((cosh(?x))^2-(sinh(?x))^2):(1)~p0 4 ~Hs(-(cosh(?x))^2+(sinh(?x))^2):(-1)~p0 4 ~Q ]|Expr|[#b @`bb#_b#_b#_})%# b$L" *|: ;bP8&c0!*Other hyperbolic| | rules}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p1 3 ~Ht((cosh(?x))^2):(1/2*(cosh(2*?x)+1))~p0 4 ~Ht((sinh(?x))^2):(1/2*(cosh(2*?x)-1))~p0 4 ~Ht(sinh(2*?x)):(2*cosh(?x)*sinh(?x))~p0 4 ~Ht(cosh(2*?x)):(2*(cosh(?x))^2-1)~p0 4 ~Q ]|Expr|[#b @`bb#_b#_b#_})## b$L" *|: ;bP8&c0!*Integration Rules| |}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p1 2 ~Q ]|Expr|[#b @`bb#_b#_b#_}))# b$8" *|: ;bP8&c0!*after Partial Fraction| | Decomposition integration}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p1 3 ~Hs(ln(?x+?b*i)):((-i*arctan(?x/?b)+1/2*ln(?x^~ 2+?b^2))+1/2*'p*i)~p0 4 ~Hs(ln(?x+i)):((-i*arctan(?x)+1/2*ln(?x^2+1))+~ 1/2*'p*i)~p0 4 ~Hs(ln(?x-?b*i)):((i*arctan(?x/?b)+1/2*ln(?x^2+~ ?b^2))+1/2*'p*i)~p0 4 ~Hs(ln(?x-i)):((i*arctan(?x)+1/2*ln(?x^2+1))+1/~ 2*'p*i)~p0 4 ~Q ]|Expr|[#b @`bb#_b#_b#_})%# b$4" *|: ;bP8&c0!*Derivatives of | |Integrals}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p1 3 ~Ht(Diff(?x)*(Integral(?y*d*?x))):(?y)~p0 4 ~V?c4 (i)~p0 1 ~V?c0 (n)~p0 1 ~V?c0 (m)~p0 1 ~V?c0 (c)~p0 1 ~V?c0 (b)~p0 1 ~V?c0 (a)~p0 1 ~V?c3 ('N)~p0 1 ~V?v0 (I)~p0 1 ~V?v0 (t)~p0 1 ~V?v0 (k)~p0 1 ~V?v0 (z)~p0 1 ~V?v0 (y)~p0 1 ~V?v0 (x)~p0 1 ~V?d16 (d)~p0 1 ~Q ]|Expr|[#b @`bb#_b#_b#_}`f#})!# b'4`f }[#! `f#}) # b'4| |}& b!( b"0 b#8 b$@ b%H b&P!WW})6# b'4" *|: ;bP8&c0!*Definition| | `f },HGradshteyn and Ryzhik 8,N354,N1,L 8,N356,N3,I| |}& b!( b"0 b#8 b$@ b%H b&P!WW}`f#}) # b'4| |}& b!( b"0 b#8 b$@ b%H b&P!WW}}}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p0 0 ~A(Gamma_2(a,z)='G(a)-'g(a,z))~p0 1 ~A('g(a,z)=Summation(k):(0):(m)*((-1)^k*z^(a+k))/~ (k!*(a+k)))~p1 2 ~A(Gamma_2(a,z)='G(a)-Summation(k):(0):(m)*((-~ 1)^k*z^(a+k))/(k!*(a+k)))~p0 3 ~sb/_! } b00& c#T"_c/__c/__!"} ^ _~A(a=?a)~p0 4 ~A(z=?z)~p0 255 ~A(Gamma_2(?a,?z)=-Summation(k):(0):(m)*((-1)^~ k*?z^(k+?a))/(k!*(k+?a))+'G(?a))~p0 4 ~d~sb/_!! } b00(! c#T"_c/__c/__! ""} ^ _~Q ]|Expr|[#b @`bb#_b#_b#_})!# b'4[#! ) # b'4| |}& b!( b"0 b#8 b$@ b%H b&P!WW})!# b'4`f#}" *|: ;bP8&c0!*Application| |}& b!( b"0 b#8 b$@ b%H b&P!WW}`f }) # b'4| |}& b!( b"0 b#8 b$@ b%H b&P!WW}}}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p0 0 ~Q ]|Expr|[#b @`bb#_b#_b#_})!# b'4" *|: ;bP8&c0!*Integrand| |}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p0 1 ~A(y=t^x*('p*e)^t)~p0 2 ~A(y=t^2*('p*e)^t)~p0 255 ~d~sb/_!! } b00,! c#T"!c"H" c%X"!c'8 _c/__c/__!"} ^ _~ ~G1 1 160 352 0 1 5 4 10 (-0.8500000000000002...~ 0.75000000000000011):(-0.56000000000000005...0.66000000000000014):(~ ?=0...2*'p):('p/5):(10)~Q ]|Expr|[#b @`bb#_b#_b#_})!# b#@" *|: ;bP8&c0!*Declarations| |}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p1 0 ~R8405120 ? (t,y):(y=bottom...top):(t=left...right):(~ 0)~p0 1 ~gc1 2 ? 0 -2304 -4096 0 65535 -2304 4096 0 ~gc1 2 ? 0 256 -4096 0 65535 256 4096 0 ~gc1 2 ? 0 2816 -4096 0 65535 2816 4096 0 ~ ~R8405120 ? (t,y):(t=left...right):(y=bottom...~ top):(0)~p0 1 ~gc1 2 ? 0 -4096 -3022 0 65535 4096 -3022 0 ~gc1 2 ? 0 -4096 -1679 0 65535 4096 -1679 0 ~gc1 2 ? 0 -4096 -336 0 65535 4096 -336 0 ~gc1 2 ? 0 -4096 1007 0 65535 4096 1007 0 ~gc1 2 ? 0 -4096 2350 0 65535 4096 2350 0 ~gc1 2 ? 0 -4096 3693 0 65535 4096 3693 0 ~ ~X2 8405120 (left,y):(y=bottom...top):(y)~p0 1 ~gc1 2 ? 0 -4096 -4096 0 65535 -4096 4096 0 ~X1 8405120 (~ t,bottom):(t=left...right):(t)~p0 1 ~gc1 2 ? 0 -4096 -4096 0 65535 4096 -4096 0 ~V?c64 (~ left)~p0 1 ~V?c65 (right)~p0 1 ~V?c66 (bottom)~p0 1 ~V?c67 (top)~p0 1 ~L2 255 ? (t,y):(t=left...right)~p0 0 ~gc0 84 ? 0 -4096 448 0 2580 -3773 433 0 2773 -3749 432 0 3096 -3709 429 0 8192 -3072 368 0 8409 -3045 364 0 8772 -2999 358 0 11868 -2612 298 0 12384 -2548 286 0 14384 -2298 237 0 14964 -2225 222 0 16512 -2032 178 0 16705 -2008 173 0 17028 -1967 163 0 18576 -1774 115 0 18793 -1747 108 0 19156 -1701 97 0 20576 -1524 49 0 20793 -1497 42 0 21156 -1451 29 0 22705 -1258 -24 0 23221 -1193 -43 0 24769 -1000 -97 0 24986 -973 -105 0 26317 -806 -150 0 26769 -750 -166 0 28445 -540 -219 0 28897 -484 -233 0 30961 -226 -287 0 31178 -199 -292 0 31541 -153 -300 0 37153 548 -311 0 37370 575 -306 0 37733 621 -296 0 39153 798 -241 0 39733 871 -211 0 40249 935 -179 0 40829 1008 -137 0 41281 1064 -101 0 41797 1129 -55 0 43345 1322 119 0 43926 1395 200 0 44894 1516 353 0 45346 1572 435 0 45563 1599 476 0 45926 1645 548 0 46442 1709 659 0 47022 1782 794 0 49538 2096 1540 0 50118 2169 1753 0 50570 2225 1931 0 51086 2290 2148 0 51538 2346 2351 0 52118 2419 2629 0 52440 2459 2793 0 52634 2483 2895 0 52851 2510 3012 0 53214 2556 3215 0 53666 2612 3481 0 54182 2677 3803 0 54634 2733 4102 0 55730 2870 4898 0 56310 2943 5363 0 56762 2999 5747 0 57730 3120 6641 0 58092 3166 7001 0 58310 3193 7225 0 58503 3217 7427 0 58826 3257 7777 0 59406 3330 8436 0 59858 3386 8979 0 60826 3507 10235 0 61406 3580 11053 0 61922 3644 11823 0 62012 3656 11962 0 62067 3662 12047 0 62212 3681 12275 0 62216 3681 12281 0 62221 -32768 -32768 0 62230 -32768 -32768 0 62248 -32768 -32768 0 62284 -32768 -32768 0 62357 -32768 -32768 0 65535 -32768 -32768 0 ~t~p0 2 ~Q ]|Expr|[#b @`bb#_b#_b#_})!# b'4["! ) # b'4| |}& b!( b"0 b#8 b$@ b%H b&P!WW})!# b'4" *|: ;bP8&c0!*Antiderivative| |}& b!( b"0 b#8 b$@ b%H b&P!WW}}}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p0 1 ~A(I=Integral(y*d*t))~p0 2 ~A(I=Integral(t^x*('p*e)^t*d*t))~p0 3 ~sb/_!! } b00,! c#T"!c&H! c"H# c'8 _c/__c/__!"} ^ _~ ~A(I=Integral(e^(ln('p*e)*t)*t^x*d*t))~p0 4 ~sb/_!! } b00,! c#T"!c&H! c"H$!c%X"_c/__c/__!"} ^ _~ ~A(('p*e)^t=e^(t*ln('p*e)))~p0 255 ~A(I=((-ln('p*e))*(Integral(e^(ln('p*e)*t)*(-ln(~ 'p*e)*t)^x*d*t)))/(-ln('p*e))^(x+1))~p0 5 ~A(z=-ln('p*e)*t)~p0 6 ~A(d*z)~p0 255 ~A(d*z=-ln('p*e)*d*t)~p0 255 ~sb/^!! } b00*! c#T"!c"H"!c'8 _c/__c/__!"} ^ _~ ~A(I=(Integral(e^(ln('p*e)*t)*(-ln('p*e)*t)^x*~ d*z))/(-ln('p*e))^(x+1))~p0 6 ~A(d*t=-1/(ln('p*e))*d*z)~p0 255 ~sb/_!! } )+! c#T"!c"T! c"H#_!#! !} ^ _~A(I=~ (Integral(e^(-z)*z^x*d*z))/(-ln('p*e))^(x+1))~p0 7 ~sb/_!! } b00(! c#T"!c"\"_c/__c/__!"} ^ _~A(~ ln('p*e)*t=-z)~p0 255 ~sb/_!! } )+! c#T"!c"T! c"H"_c/__c/__! !} ^ _~ ~A(I=(-(Integral(e^(-z)*z^x*d*z)))/((-1)^x*(ln(~ 'p*e))^(x+1)))~p0 8 ~A(I=(Gamma_2(1+x,z))/((-1)^x*(ln('p*e))^(x+1)))~p0 9 ~Q ]|Expr|[#b @`bb#_b#_b#_})-# b'4" *|: ;bP8&c0!*,HGradshteyn and| | Ryzhik 8,N356,N4,I}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p0 255 ~A(I=(Gamma_2(x+1,-ln('p*e)*t))/((-1)^x*(ln('p*~ e))^(x+1)))~p0 10 ~sb/_!! } b00.! c#T"!c"\" c#L"!c&T"!c'8 _c/__c/__!"} ^ _~ ~Q ]|Expr|[#b @`bb#_b#_b#_})!# b'4["! )## b'4" *|: ;bP8&c0!*Definite| | Integral}& b!( b"0 b#8 b$@ b%H b&P!WW}) # b'4| |}& b!( b"0 b#8 b$@ b%H b&P!WW}}}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p0 1 ~Q ]|Expr|[#b @`bb#_b#_b#_}`fb#@}).# b'4" *|: ;bP8&c0!*Change x | |value to recompute f,Hx,I}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p0 2 ~A(x=2)~p0 255 ~d~Q ]|Expr|[#b @`bb#_b#_b#_}`fb#@})-# b'4" *|: ;bP8&c0!*Number of| | terms in incomplete gamma series}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p0 2 ~A(m=40)~p0 255 ~d~Q ]|Expr|[#b @`bb#_b#_b#_}) # b'4}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p0 2 ~A(f(x)=EvaluateAt((Gamma_2(1+x,-t*ln(e*'p)))/~ ((-1)^x*(ln(e*'p))^(1+x))):(t=0):(t=x))~p0 2 ~A(f(x)=87.176544496812582)~p0 255 ~sb/_!! } $&! c#T"!c"D#_c/__c/__} ^ _~Q ]|Expr|[#b @`bb#_b#_b#_}))# b'4" *|: ;bP8&c0!*Check ,Hintrinsic| | numerical integration,I}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p0 2 ~A(f(x)=Integral(y*d*t):(0):(x))~p0 3 ~A(f(2)=87.176544566363887)~p0 255 ~sb/_!! } $$! c#T"_c/__c/__} ^ _~c2 133 -1 131 -1 132 -1 ~c3 136 -1 133 -1 134 -1 135 -1 ~c2 140 -1 139 -1 161 -1 ~c2 144 -1 143 -1 139 -1 ~c2 145 -1 144 -1 146 -1 ~c2 150 -1 149 -1 148 -1 ~c1 152 -1 150 -1 ~c2 153 -1 151 -1 154 -1 ~c1 154 -1 148 -1 ~c2 158 -1 156 -1 148 -1 ~c7 166 -1 165 -1 161 -1 128 -1 163 -1 118 -1 136 -1 1 -1 ~c5 169 -1 168 -1 161 -1 128 -1 140 -1 127 -1 ~e