From: Subject: =?iso-8859-1?Q?Gravity_Concep?= =?iso-8859-1?Q?ts_and_Applica?= =?iso-8859-1?Q?tions?= Date: Sat, 14 Jun 2003 15:08:53 -0400 MIME-Version: 1.0 Content-Type: multipart/related; boundary="----=_NextPart_000_005C_01C33286.DE8EC1D0"; type="text/html" X-MimeOLE: Produced By Microsoft MimeOLE V5.00.3314.1001 This is a multi-part message in MIME format. ------=_NextPart_000_005C_01C33286.DE8EC1D0 Content-Type: text/html; charset="iso-8859-1" Content-Transfer-Encoding: quoted-printable Content-Location: =?iso-8859-1?B?aHR0cDovL2h5cGVycGg=?= =?iso-8859-1?B?eXNpY3MucGh5LWFzdHI=?= =?iso-8859-1?B?LmdzdS5lZHUvaGJhc2U=?= =?iso-8859-1?B?L2dyYXYuaHRtbA==?= Gravity Concepts and Applications
Index=
 =20 HyperPhysics*****=20 Mechanics Go=20 Back





Gravity

Gravity is the weakest of the four=20 fundamental forces, yet it is the dominant force in the = universe for=20 shaping the large scale structure of galaxies, stars, etc. The=20 gravitational force between two masses m1 and m2 is given by the=20 relationship:


=20

This is often called the "universal law of gravitation" and G = the=20 universal gravitation constant. It is an example of an = inverse=20 square law force. The force is always attractive and acts = along the=20 line joining the centers of mass of the two masses. The forces on = the two=20 masses are equal in size but opposite in direction, obeying Newton'= s=20 third law. Viewed as an = exchange=20 force, the massless exchange particle is called the graviton.=20

The gravity force has the same form as Coulomb's=20 law for the forces between electric charges, i.e., it is an = inverse=20 square law force which depends upon the product of the two = interacting=20 sources. This led Einstein to start with the electromagnetic=20 force and gravity as the = first=20 attempt to demonstrate the u= nification=20 of the fundamental forces. It turns out that this was the wrong = place to=20 start, and that gravity will be the last of the forces to unify = with the=20 other three forces. = Electroweak=20 unification (unification of the electromagnetic and weak = forces) was=20 demonstrated in 1983, a result which could not be anticipated in = the time=20 of Einstein's search. It now appears that the common form of the = gravity=20 and electromagnetic forces arises from the fact that each of them = involves=20 an exchange particle of zero mass, not because of an inherent = symmetry=20 which would make them easy to unify.

Index=

Grav= ity=20 Concepts
 =20 HyperPhysics*****=20 Mechanics Go=20 Back





Examples of Trajectories

Common misconceptions about guns:

A dropped bullet will hit the ground before one = which is=20 fired from a gun.

As shown in the illustration of a horizo= ntal=20 launch, gravity acts the same way on both bullets, giving them = the=20 same downward acceleration and making them strike the ground at = the same=20 time if the bullet is fired horizontally over level ground. =

Bullets fired from high-powered rifles drop only = a few=20 inches in hundreds of yards.

Fired at twice the speed of = sound, a=20 bullet will drop over 3 inches in 100 yards, and at 300 yards = downrange=20 will have dropped about 30 inches. Plug in numbers into the bullet = drop calculation to see for yourself. Ammunition manufacturers = contribute to this misconception by stating the drop of their = projectiles=20 as just the extra drop caused by frictional drag compared to an = ideal=20 frictionless projectile.
Index=

Traj= ectory=20 concepts

 =20 HyperPhysics*****=20 Mechanics Go=20 Back





Drop of a Bullet

=

If air friction is neglected, then the drop of a bullet fired=20 horizontally can be treated as an ordinary horiz= ontal=20 trajectory. The air friction is significant, so this is an=20 idealization.

If the muzzle velocity is
v =3D m/s =3D ft/s =3D mi/hr =3D km/hr

and the distance downrange is
R = =3D m =3D ft =3D yards,

Then the amount of drop of the bullet = below the=20 horizontal would be
d =3D m =3D cm =3D inches

If the gun is fired on level ground at a = height of=20 m =3D ft, then the bullet will hit the ground in =20 seconds, having traveled a distance of = meters =3D=20 feet.

To hold the drop to = cm =3D inches at the downrange distance R above would require a = muzzle=20 velocity of m/s =3D ft/s.=20

Index=

Traj= ectory=20 concepts

 =20 HyperPhysics*****=20 Mechanics Go=20 Back





------=_NextPart_000_005C_01C33286.DE8EC1D0 Content-Type: image/gif Content-Transfer-Encoding: base64 Content-Location: http://hyperphysics.phy-astr.gsu.edu/hbase/images/gracon.gif R0lGODlhAQJXAdUAAP/////w3//jx+/h0e/Vu9/Sw9/Hrs/Dtc+4or+0p7+qla+lma+ciZ+Wi5+O fI+HfY+AcIB4cIByZHBpYnBjV2BaVGBVS1BLRlBHPkA8OEA5MjAtKjArJSAeHCAcGRAPDhAODAAA AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAACwAAAAAAQJXAQAG/0CAcEgsGo/IpHLJ bDqf0Kh0Sq1ar9isdsvter9SgXhMLpvP6LR6zW673/C4fE6v2+/4vH7P7/v/b0KAg4SFhoeIiYqL jI2OcYKPkpOUlZaXmJmagQCbnp+goaKjpI2RpaipqqusrZOnrrGys7S1s7C2ubq7vL2GuL7BwsPE xMDFyMnKy6LHzM/Q0dKEztPW19jZaNXa3d7fyNzg4+TlseLm6errmujs7/Dxh+7y9fb3dPT4+/z9 Y/r+Agp8B3CgwYPfCiJcyDCawobqFEhUIKGixYsMJhKAuOwhR2wGFECQoEEDiBAoU6pcyTIEiJIS ICgw8LGXx5rMDDigoKElyv8OGYJGGEq0aIQJQTN08BlCAwUHNHHe6iT1m04LHlZ+yDAhQoIEAcKK HUu2rNivRzN8WAnCAtSqrG7C5WUAAoeVGSIsKGC2r9+/YQssiJBhJQcIUeeOkqu4FgMMKjd4BUy5 8t8EETaoxMCgcSjGnl05yIpywwO+llOrLlvggWaUHhyE3gR69pqKmBTcDfGhwoGxB4YuGLC6cgGw qg9UWBuCAwLbl2pDR2Mg6kwz1wUo0L5RDILneySg/BCBuNgDr1NOKA44QoiwAxKYpzwgAnMJ0ylJ z18GtwaSnYlBgFMayBYCBhJ4QJMFFlCAQR4DolTBfGEd8MEHDRCnXAgVsOf/F2ZhJRACcpYNUAFK GnTHHyP7rShGRQgoSAB4AkAgmwAcCBDCRjBaIIYFNNZx1wcLmFXYb2OdiKSHH45Y3AJr5ejiIi26 iJtdHAQogAbbbalACC9W5EFJHkBwBwW8LTmWiOuRVUAGDVSYwQETfADWAoWFIFlYD8yZZIcNZBBA A5ptMEECGRQpVgUd9mVhCBTsAYEGkwpAgAUadCaTpT4igAEGzzkAQYMSWACqAJ6e2lCVK1YkkQAG gCmGjWLkKGtFO4mhQJByfPmBmmO5R2JfIm6w1QELhHDBVxOEEEEAyT5bobMBuBdAAidWkKGyYhUQ QpuOrtXlHQ48CAGYXBKA/4ECDPi4EwEcGECABwQkyAAFHMzogQD0GuDjqlRNmUdFBnggAQaRCkig gWFuSQFPKs5hAbV9FUZZseZd0MFYQYXVwQZiNcuXtdc6GcAFH4j1QAjAluXev3esK0YIBmigq4/7 guqABRJZwABuuOm4ZYER+zGRRBclbVFGE/HCKn/V6cqrdtaJETWq49aRFYVkWSxWnigJWrKiZQ0A VFgieyw2ySIi10AIiipFXwj74sHzzDXfLACQOZJkEUX4BS0rAhQoaAcB7FZU0m5MNd7SmP9JkFHR qDwtsCMo/eV1hV8lsIHYbY+1wAVgi31ACA8EcHqc1b5XMnIDcBhA7OD+hf8SglnL8ZgADqCrgLrb MXAYrPkCDzR+OhZMwLyJtWHAzxj01PjnQVVg1PVEkR5Uej5pgCADzX8W8OWxbO2XsGZ9HqLJrUvW wAEdewxyneaxzT7Kg4aA2l+xx2bBXU4Bn+4oBaZLZWoMGrBO9DrjANk0UAw2e8wB10CAn5mEJVu5 QAQe8BWuMQk+X3lABEjXPclRDhOWI98iJiYts5yuUWPxFujY14ELcExsAViZ2WBoPxK97QAXABll XjaGCpKEbhaAwNTOwAAzlSsRCsAXS7jCQQ9+UDXxeQBSWMIBCuTOEilUYSJi9Su/HGksAyjMDEn0 rfNspVvfYl8Px9Ib1FH/5lHhGwMCIIABD7xEAr9DQ700YIET9qFdJ0lJB7TVsis68jwNqMBSUtIW LVUijFaSEqoiFTSjWeAkZTRLAdZSga80oAMfIN36SISyBmDmAx9bUmE2Jhb7RWBJJ9IfYB6VsDU8 T4pdfMsiDCCBRPJGW/t7pDL/UoBIMsclEsijKcYnRjpcxwDDm1W8CEajkNiBmB7wAAWwyRuykaU+ r5FMfNoEvyUN4AIoWRaUbBgWPKVOLIH6WghwmCwc9gVKdJsDRUwCAgxsqhD+SklvzLnMhlZmActJ iQWkqQhMzmZAPHGAAjwAM6xQpIsI491/EiiHcoXAZ0WU3gWs6NDieIt1/2YxEYpAYKY6IGBnWfkP AwxZBwKgKWwwbalQLROolFCAp7+gZjXhQCsceWkMCrCZBBIGJimJ6g2EA8FhTige3pRnqB6qU1/q cx9UtQVCFkSiA5YYhxiFbVhgjStgEgBPurE1qUulA5cgGNVxRVUAglPASzTAgQdR0C4goMBdvSO9 3jRSrmURIXnKohzmaIBGCDgrH0SCARD88Ytt6J2e4GqWzpl2rg09AEtX4zmU3IhKSs1rG5qao73q SqrIo5mUnqeGdh3otaEljZ5OA1m/NGCDMXRNSmJjBnjBrA86ASYFBMgGBqCkdpoLyj7j5xfXUaYB Qa0YaZnknhBYEhEWDf8NRgv0VO94AHAzAyyCnHMGAxTOYBRlgwIgkxJDjbe4IZoA92QmSA489w+I IwkIPGBQthLgJOGtjHfhg5oDNPI4ZJFPWIbSLWANIJnXSmYCQPxdlyD1D+mdTXYQEDEEVKdqsAok GQjgAJPcDQ91YVzY9ELilgqGMIZBDBucm4g9YqUpJhyDeLBrGe+OkDwWyoD6AuC6CnyuA78ZwAY2 0AGvoORZktwycZ5MGLAcACgdWM+ZlRJhwDQLeYlIsWzPgIBPcsABJ54DjY+skq105Svw8VB8MFMB tayEo3iGA5GHea+eGHg0uiyOkzvAF22FZQNgeU8kw7LpCqRuAB+oz7P/GkDPB3QoApQOQAbAsoEs b6AAFyjSO1fjrbrFObZzJkRdwjnOQ0T3gj5JSlewN5RCB+WZLHGKMPXMgXw9giL89ZCTW5gAyWb6 ZNYbysZSFqxnxRo+KeOwqhNwZqLAaQJpZmiTZXVruITkaA5QmrxjcrRdFeIxBzqvIkIykpIY03E+ GSy98ysHeDlbElnpMWWmjba8eO7aGcg2hydcrWetWizvEfeqE9BlotxJwB1YrSgDWlFc4+PdFikJ sAHO8pYMNnKAzE5bKbBgCORZEQ4AwXOOFr15H+0Q6jq4I8QDQ9UwnMpi6cC1xV0Ai4MF1E1/lhbr aUONgyXUGy7AoS79/9++NKuX6DX5Ovh9sJVPLylCIbba0a4Ulr8EQTKhKI050JbFOiLnU+skJf53 c0A8OARtBszRM6DBz3XoPaPsSquhRR6u5HDVWq4Aun9j9QAIOAKMglaXBayat4Gg73uQcy4QAD0d r+RzGoyAK0cM2eMk4LgjbLtPCis5BChgYuzdRO9Aq/e9C50R1m2jakhUANQMoAGnOUDqXDeABxA3 MHqBDwdnh3zUFL9C5sEM2YKTodQ0y7wsEns2bsqTlmzFegvQMIBXE5/BFBrZKimQ3R3xJeCSofe+ B70fRItphyaA2+tnGa0VAvYXduCQYNLTZ1zhSgE4VK+HFPCHZDI2Cf+ZVYBKBmeX8D/zNwhutU9d VxyJ0oAXkycesIEoJn7MgABHpIA8JoIB+GOGFn8SYIJ/UIFq0Hs6sXc69wg+lRJw4oJyVVQocVSP IHqhUEGfpBKL9D5A2ISQJEkqUUn6hwc2eIMYqB02Qwk0R4N/kFDjUQHq5oQeAlHPNFGvgILDgG8K dQHPJ4Zu2C0PgDKboW81CAIW2B/I41MGZTOpAh4MQEgzQgESsFaf8hwGJAEb8YeFhCqF+CL/oQZ4 NwngtIYNoHBvKEqk9kz4dUlo2Av2ZUzpdomiaBYLgG6U1GuAUIW3gTxuIQDRAy/yQi/lQgCjUn8I EC/z4lNmkkTYJAD/TQSLuZgrgASJO0gJiKSEjDSKwBFJk4QSlYRCnagLf6hQE/BYyqiMdPJME8QH mVVTbBA0IHBbO9Mz7eJXNjOOt7dTP8MBiPiM6OgzgqVYbBCJlhBFprdPE1BFQJhFW2QYXkQb0VgL kBZPYXiNBik6dUU3dzgHBqBZbRA0dRNVfuMqMjMjfzWRgPQf8OWL/4OR20FjTjGPIABakmBEZueD GsRB6qdMgyZCJMQSf7RToGCEkxBV4zEBlniQOhkYdYIiJKloBgYHQUMBZhI92LQ86/JEI/FXRwk8 n4dNg/ggMdKU65JENXJgaNA7C0kJz1N2jkM9hKd2RoF23NMS3iM5/wSXCTTpCJcyHl8FgmjHZKrB dnK5S3V5RapVMZVBViixiHSwaG/QSX4TKfs1QTWGiISjKwvki4SEADYzKadSmJ3hU4DoBlpJCojz MyRBWC3XchwAE5IzgaqwlowgWNclcoJnWtYoYapZHIgiVBdnFhTHP9/3XsyGld94haCgiq1gexMx EvPmKj+3C6SJc6WxmhJmFn0yAcTRTIERJ81UimMxmy30LM0UKMxZTxGHJ7NDGBXAF9GZFyYSgrOD FF+VAIORAanDcd8JLYXGOrO5S6+xlWcAmEKpm7tph3eQmJ5RnIgwMRRzRSPSOcQxAcuSGdcCOoLy fz+IcaZFHN71Hv9sgijP8n8LsABncwGH8gAbIyKlxGUNkCx8YRrYUnWAh6FfsUgFcGbptwFxEp9D NIRvYJ/3mQq82StZ2Bj+aQjngiHKtF1BoVoAGGuvmaDXQkvTiXa/EaFHGiKCYmmPVy3wIaG0dBRh sWrSeWnV0igcdnGAZnnPAqPftRb0KSCFVQf4Jwo3Cge68T+RcoslQRM1dmdkgC/D4z0YQF/1sKOE 8CUss0wUV6QVV6SvKagYVxZMSqiCEpuvGShbIaFrIy2rVl4pgRnS0qVPpzFcFqZMcjoh8JNj0GxT eH/4mQbLJgmZhZttsFEb4RybghufVyNF9C/oYia7s6cBmQpZcU//P+omSKotRcqdhhoWs8l8kOqk AQCG2lkAqYZ0RWp1DQAulHepTpes1Ip0TLIytoYGfGcHaZoGtkUJqSpQWcglhENYgcNRWcNHkPFU f4WrvNA7/vRIs6meR/phIadlCzqv2DoWWJasx2qknjMA+npmBNssRlpxVzpiZfSa4oapJ7OeXdav HlIYC9mt3lqqaEApCEOLH6mqhXCLIJsG78oltlkRM+KLJSgGsyg0e/Wu8sCngAAZBckk/PpOeoIk zdIB0ao6TMavDXAh+UQnFdImQZtm61EnPHsBF0C0g8I61ah5ykIc4MVpcbIy5KYZy8Iy/LoayWJY ZoCxGQsH3nOV/+3CO2CnCDSqX+W6UQzgAAY2LwzAAPTCslUJAjWzHTAbDzL7ByeBmjsZuILmEmcg tmP7BrYVjjnDhX2wtmqQg7xTHYNYL7AyEs0Tb8+jAG8BuTGbq6WQOYIbug2FEmH7e4frBra1Lz6z rY3guALTt35wEqI7u44UO+FIBoZ7B9+6sT4CAZEiPN7Ig4U1qooBu31As7SbvOzxtbhbjHqwu2cg iI8oBoZDCQZHvHBhvHwgr8rbvalhsWNAj3pQZzBnERq1gXljCQNiui6ivXywq9c4aJ2Tk96rnM0R vs5rUwcjXI7DYMNoBo7JuIaQu4CQo/cHiWWqDO67B36KnCLIoP9JEXj160Io0SXiOwc7828hABSp VxRB0YzOiAGJFgoEbDRnwG5nAL3MsMB70Ds+KorDCkKUVSHJhGHd8oFOGLQEyLL5Cwd1BoqehsNn YWrNWHckzL5jYKdm4phdhCqEFSkDUhIboRtNDCZwG5RoEin4slc19ika+wwsvAc/1UJuGMNBqxa/ 4TnqE2ZiY2VK8RtuvAGA24DlhTwX/AY2+RNR26mm6JOg8D/SdCnxxRm8oy4MdCl6izMbMVFgsoh7 ZcX4AS84shHTiw1h3MLH+YYQ3DHMqiEd6iSkdqULsGmD4htC9AA1K4Lo4Vo8LMB5zCFCPHy51BSg OgmftETsCib/dCvCKsvLtysAOmfAumwqIyk0GGABYlJjDZMNl8zApJGdTvhwnZND4NJqRbosY3EB EkdpqdSGYjgAtWnB4KdoP/Ut9MskWidR2DvAPdyyYLIdjrkp8exssGhVsVIwNPHIrigTInGLYiCI 2tDMe9CWXjXHDjiv4jZuRRqbVypx1hmHH8Cr+2gffdkdCLDDbJpI7SlXBZBLxbwJEJC/5XJ7eEsp uhFVMsEB7LIuhEwpwpM875UgBmJ7Kq3MScQAIPDFK+y5rpDHH4CTLjis6AFuCatxsAd9yqGdTah1 ljUua7oGP6V0AchxMqp7Ih1NkxNvH6nVuvK/vGNzgKUdgHRT/74oG8QE1l+dEQHN07EwkMqSykIV w4WGanFSpIlnZQGQeJnxGxtgPRsA10M1OssFXE+dBhHyLQbdUOCMIutMCHfcn2wtC6/sWAA2AI00 GEhi2WLRfN03O85nfMflwA5VWSkRrt6hnzM6JBJcXDqMxJTw2MUb2WxgwA9EBvyJYwlsBp+oSBMA 2BOsTBBVxKho26jtBvCSJm74KK49CZc5GymEwlcDVQZsB3urO/w1Hmx4zr9NaxCtEihFZ8XdBsf9 apdYAJqx3JLQ3JCdByhFpykSAptZL/iBJRplYE2sR595VDEyI/kCt5QiX+Fkh0wMdnBKUoZ9jIqU jNvNHgfAjP9R6DM8lVk6XQbHHXJ9cX0NaDbN0diDgNO5zRC1cS8PFim28hxECSM2Azx1q6eTDFiy USpckr4JRBKIYzOEPMI1sh0qrEcrqFB5sRcL7hcwCH//MX8PNrKFi9x9kdAB+ChI/giFXRO1MSBN pNKRcisWMRLSzVfuVREMQr29GzkFght/tcuEzRPs2Cs97uMT4EqJbZDxEa0xKIO1PGNByVQo8YEJ vaJzBWJIYmFotJKUhRLBiwk36pvxJm8aZW/8IB1FrpFCA1jmmzAZyeWootLsIhu3SC+1qLnw9Vfw /N/Uq+MTrgbkl4AKiH6CPorth3lzHn9PIcCumwYNaUd/0aX/UnY2E9AoCwAya5ZmxHoi+trXnIZm ErwyeOsJveOVnRl//7FWnfu84QgBdYPlKOsBTcQzbYtAMkHIKj1VcvuHxIQfulEzKT0u2A63T45V 0MO/K8HBQ7F62o2XpjQUpAPChvE9Amzn614GPdG1ZNGljYJlFhIWlrZ4WsYX1DJ1yVp8cqw6QlQx TXEJFVR+LUE9Dl0UxlaWpT1dHK7Ask0GOQi5yPNztGjWN3KqXE3WgLU8lqsdXSITNObVsDK5pd5W dkh20aPBPgEUcSmW14MUaIfvAXeWcTfQdw4H1vUB5wyx4xYAHTAcIWDZHUcYL1pPvdF9fUIUzSpK a0GHirBH/6ZXQ3oRy6U1GBoTZPveESEfDVH+bsCpcjzf7AD3cn8jcwiW9HCQFWR8PtX69Ka2aRxX FNdWIYRhJ4RRFDnpHqw7RtQeGb395iVSitxTJmkpDQL9CVHuBu82EZoZnOZbb5dPCPAy3ZbJG3Ps 9BfHrN8WAFhXLQrPaff0ZzhUdDFFpouwXypxAZ0NWceXkAdS52Dc9ikY3tBAWMR7F33v90/f/BoT MpKRedjKrF2RahugQQ166/eLCG4NJ5K/TMcHNsy11u+w+chQwmxw0VNvGdeXl6pjHnx+FtEXInDY hqG9lyix9mxKGr0BBIXAkFg0HpFJpbFQ+YRCHoWAWrVesf9Z7Zbb9X65AADYK6GQuxQEuqp2OL4a thUBgs/xeT3ewiHkKUIqlggLDQ+PKkLO9roMMKA+IgYQKy2PBiKeQjAMGj9BQwXEQkNENabmEAgk JL5M8eruRBsV5KpaweRy+fz0PEIWLoeJlRaiaK8cQKAmKIuhDwcmoOySr7G1SD8Dzyg4ONY0LEAI vsMFvlGtKMY5FAg0NDoFHDQ44BTAz8ZBUCUwYNAABwEHDRQIEBAoARYbWdmorIJHZcoaAhNXUSSw RoABA7wUeIrIMWIIBK0MkLz4h0sflngMQIk2s9gTkcksQNlwgGZPQgc2QLEAkei1bZ9MOXBFgIOA gwIguFL/IEGpAKZVEGCwCkKBhSldBZSDKsDDHwsGnv6TQ8CDAF9UIUAQoKAhmYdENXiQwIGBgBAH C+5FEFdAVlvpMHyTEI8CBrkUKFhgVC+EUg6NzwRep8XlHgchMvgUbShD5WRMoUQYvRpJBCi+isZu dLSRKQypNCBYd7sKBgutPIjkhQpEKwltj3vVbWXdP1dOIeiVYMHC5rpf7uKFY6BpCE/0HnFP58DW VQG/IdxpynWuFVNmqNj29Ihz2UaBVLPWX8T1ZFCoPxBmvwEXeAI22RBkg7Y9TKGgL7fimcKCvgxw wDEFFIBAJAYYeYcrDBdbgwEPGGiqHrSmcI6Kd95RgAEH/xy06roussMrFVNgacgUP/yw5TABWrlH HhAQYAADvdwD8jkc5dEAhCwoIPITDYKxZIInNhBwwCWOueU/DkL4gCfSoAihgwmUyM+QBBIIIIHQ kAjhJwNfStDOLhbUwxS0GIBvHX26Iu8de6qIhwEIQpjKKzPYYmDEeCAo0akUpwLh0KE0gEABDBjQ rasZt6gRLwrlgAU8raIa6rC2zpvuQQcQgIOpVPxSMj6yWJJLGSk/AbNNRB64gJIExNxyiQRCMBGU nIo9JINfB8gyCTkPiUC1AcY8gtolDnhiqDvB3SLPPJ776A4HRPoolY8gqJOA9NCdiyoqDIhKJAfa PfFEF//Tq0KpdSWYCgxR8dIrt1oL40CwjiydSw4Lo5SAu+mGuuwbK+zgxRQGNJBgoF1Jqm1bZ38N 4IEGApgmgwYaKKAAlAN4eYhgL/i1gQMq4OmBDCoQAhEoQkE0hGxJK9nalC8IYacAqAltgKQ7EAZn RTYo4IAOOrgZzac/kGSIkZXoNgRdwy27inHNTlsLgm3MqD0qVqoilY3oRcAjikhCgNa67377opuo WCZkkS2JYIObi+A5AUXYhPNNk58tUIgMzixgggoSeOCDSoD+hABmHrAkgwfYLJCn0d3sANsQ2lw5 gG4HQFaYyweooOfHJ9i6A57AVuKBEMRSO1y0hS+ebRv/i8dCcFpkqiST0rwuoAMiOmh8iMdbHmKD 1lGOlogJSi6k80YYgrOSDDbIgGdhpCeiApTlLGB7NitYIIENrg/t6McPwDaB6gPQOyWU5jnJSxDx DFi24xHFbQlcHvMEeIgFRO1xQ3hWBfmXgQ9osHVtQlaZQqAm8YGKDZ9j3SWeZYQKBuBociKW+tTX AAzqTzXY22AEABhBJCAreAmMDQJ9aKcFBrEoD4SgJULwDBZGQH5EuCCcFhAaAAYghSls4hAKoMQR fuIz5jtf+FK2uSFcQBhyGsD0hrCAAsxwiW4KzQeesb0Ans80RCQKEAfmHy3Ey0t2HKIds/GZWdDC V5W4/0AFKCE97gXgGAmQ3gCi9UaeNOCEKQxA1mK2AS0eK1mfyEnoUAhGptXMcF9rHeYaEBo2RuB2 UiRdBToQOh0igZLfAiQ28PiFH3FhHSRM3h9vmQxg5oFKWjJE7bAkoAOUBn1tokbW0NSADnxgAppj 2piWqTSiEaJLvRraMLJ3hJ05Y2ZOi0AGyCmzmKGsABdoGcpwRsYFXICFlThAJ4NplDF8Qh/VQQir JhQ4EHTHYxr4gzr2pkBrmG0VdsNKyEIit5sgIG95m5tEWJLQiCwUG/gRjSWN1R+kzNJYxhpfPkWR Sy8oQCy5wcAaWEWFXq6BAulZirIUOshw3WMvfaFOY/86chC+MMYx6YiMN46KmG9cxAPgkEtWsDBM PXTxo6LUT2l0iofmlZSrRjgpSkGh0i78qBUwYoAtJ4WwVvgGOIC7k1RH5TAEfMsCJ9kOvtQTlq/o tT26alFbxEMBncI1DzEhqSX6x1UouFWrh+0qa74K1tnssxa3cBBbKLC3XlJhrZrKEGMRRFiI/Klj HpCHByCwGacYxElFOpIrjISkdhwJQ7fggAHsgxWOEgUYxnwsNI4R0z2AaZu/HdA9cSrZyYKCLpEy qAAEcoVMqTVgg+ojGi7iIuNsVwIMwFCd6LDbtJEWRngTbGFcFbhYWQUfsuIABEzUoltAIDLhzWo2 AjH/CONGQxF6zMMn91vS36FVuXsQKxcqhC+WlJcOrngOhjoigXxhRyl5AeGFMVwm01JlDaJF3mEO 0g4CTAwVE6OOWyDTFIv5QS8L+ZEBGrZR/0IEAVDYZCWsuqUBQGFwefgM/oqRAGsNOcf7xWqBw0pZ WugGtHqYCpUwvMEMXGDIVY7ABdS3iQsPVKMM/QPdCrO3ieANK7TSG9zgsREwu6VQHCBwbMAkQiQa 1zXJ1YMJi1yIc1Y5z4/lIXiRjIcDk8EBD2oEASzEjDJ1gMoLKG4hDrCAK3cAhCDAgAMAHWgwGOA3 cHMzuD4DR2II8ACPpskAnnBfcoGmGEczQv8a8ACf/70uAjBz0wBCN4BYx85qREjAjck0Y02jYdAJ 6oqizVS/WdOkAAuAZZlA4JVhY3dunw4XMOT8s1dvMH0BSGXKqvQA/Q7DNcL1HOiI4erEnQmWQ2jA Bq4MZKWFZgNUpnS3sChGS/yuh9OeQ7Fj4wBgQCGWphbNASZAaSh4QNX+zgJT3pwgBoRp2douwvu0 92s5LWADaCIjMQrwBEMHDQoGX4JrQNi6/MhRk2PkXZuieD05Rc1k40bEPcfm8DwAHCICj0TOjIuz TTDcjxiaCne3a/QetznidqKSFy1ehMxpok3bmwDHA6BvFP4FG8wyeRLU7cRfXVDKlJPlENQtp8sF QP+O9nyCVnQuaCWnTQEDlwSwu5qJoXc5QQaYSjvAlGHBY9ggFAiYASAuPBiHAJScM8IEMhCB+7XJ WhmIVgLoOQx+N/nQYGoWIsJuwbEnAChsYpMQqPUANcWvA+1ze7IyHXcv8JwWConEJAKMCU1AAQOx x0aF2jH49E3ZylbGMvoGv4h4pU1ofdaWV6nXpgNcAH+QbzyOoUC2awDIt4QIPRVHn/UxZQD1WFQd I6m1gQqgCREFgr3s5a42ljYD77lPGTWAx/dQINoCAy/TBquJ9KDhADIH8rRs4SwA08rG6zgHhjJg magsffTrTNCv4gxBbJpOFFAjhEDvwkLDklJImij/B2a2BYeQb2ZCwALT5DV8D/7CYO7uRGimyP6O ReG0LxTqBcrKJPIWoP5OTdJKA4QyhfOyATXO7xBMj00gKdasBpQOQAhi5xLO6P1iIye0aTRi58aw ZY3OKI2ADNKCIgQy0AXxBAYTxAoRiQaPSRHEUBQsBITgzfn0Q8jCkPcaDhtQY2nUMJOoUDYYQNHS cEtCzn4uAE0wz9aUYBqq4Q7J8AUXEAqu77d+bd+E4tAkANk2QNb2MGYeoA6LowVrz/O+rqTE5kAQ 5BFuzwdpQsgiAJRakRD0jveIsBEdEVysEBEHSA6tZHcugZIWobCs0EyYaBOPoABwqEzOQjYABBd/ /6sB6KRs9OHnVHC/mmDvaFEPaG+qoIAZkwCkfMIbK8EXGRELWEHRDocYCeHdqmExYiMe6M+4FPEv QDHg/G9lVHE/dC0Io2Acr7EW+44Zsi0XjUAdH7AA4GQC2CnzvucDMMkZ9fASXAMEZtEK6g4KwBEd leB+Fk7/aCEQzEQXe+J/oEDYwmVTQMid7rEndC1pyoQ3+tHAzBAvWA0RvBHVhCBYLoknOiA0GsDm WGkA5MeRMjElu5HrvsAjP4AbMXIJnHEkZWP+BGEaRaMJqoEjy6Ze/E9pro4onWcBJqAOo0BDXvIT snEO6OIDpBIJarJ/hCw0KoB0Ei4A6qcIWs/dBv/hIish5BKlCzaQnJbSEuLRFIvQI6NSP6hyJOcx bQYj8Bat0UBShSTtAhSuTN5r6cYy/hKESgJyCWpyA9SvAkJjnmoNc47wa3ztAx+zNYxybZghQAqh E0FjM5NAlKCOW/CuNonA/TzAMpPBFsoEc0RjccpEtfKJADhEBy9s+Cqg+KwFNJEvww6CARLzMsmg LNHAsLhS9IrgAdgv5s7oAl4GNI1AD7kT/KJhx7xDCxbvIX1HjuSH/Qyhd2TzCPByjsImKCQSQXyT 4CZgFLkl4YbTKoMpVgACOZMPw/JiIHhTCyAMF5RnIuPOOskAUWzOWZbTWhLg3TIUfYSA+mKG8Yz/ gOMWQJomJzWRQBFu0NOUJiU/zyCHAGdch4UwD+goSTVuJmdU42VSyS9hFGX+p2cYCTRJEBaDQjAZ iBwW7S11MXOerRrqqhH1RgGUAumoAkNIwkLwgBc4CwuIsx8lFAwgQSmZks8gxxk+LkPRzgLnCei8 LS0PgZLg7gogoeUgDY2YgIIyMYCeBfK8jQMpZwIKwIUEYXFCQ3rsJxN/1GrwFH4KIVra8E4cAElB aCcjz8rUZzKdlB+pE27ScwsMIDOGYjDMwAJeyik4q2Ogwzemc9i+9AuAwT//MgmQCwvOElZXqAiu bggGIDRS0DTtM0ZdyE5bL1dTBjXd5FcmQDUc/0tsBDQbBuNIDlTDHGNBN1ULiooLkMMUbMoPEKAt TKHTLm0coGIMda5VvWCrYnUYIivObu4Lr2dXL8w+7ZNaLMmFzOdZ9FEmUuhpOmADOkBZq2U1FbM6 kI48qLVau0BSWsIWMqsTNKZWhIu0XtJcuwBd0xWJrqPG7PQQ0NLXNmcuX1ReqYVef8VeiaBqQPZ1 zHM50Q5gD4HSDlY2tFQUEIAkqUANZI9XtOBQNKBPdmFJauVJOgJFHGZiYxIbLPZif+Y6AgE+q6Vq Mil03o0SWogIRlY750h2vI0nW+5oUugCQud/XNYQqMFmE2RmQ2GX1mZV80kyuIAtFuMybKVWvv9V Lm5DYr30aK+BuJQWsfCpCqjERI/xHNGua9jvXsdI7cbPTdIHNMZEE6gJBUkvKGpmaHBzNgXWbNA2 C+pOHs4AIKTAAcCBIOahOn6kxJokQjwGA/ChHpqkgFCq7rrgSXH2DWTKVFnhY3C2Zo02QcJ0GHDt AlCS3FgDTq8gaffrVrckssJlc2m1pU7CoNBCph5hDTzmdDdlCpxrKrTic3DFKWAXpaQAYWmBYrmA QqWw3tiE+rLTgny1J1D0eB3LWJR3QJgXXJz3CsjKOKDiOSQMFnzkFoiDOY4uPva3wOqLfEPBfD3V xgrH5lDHZdjkdR7gASjhCXXVg16HdTA4ZUz/VFcXS373EFu66n7vJH8p0rL6BLYYwUF8gWN+5B3s o7YK2C/MA4XtCMYUeIH19ho0U3QezXCyZoIi4EqC193oSe1AAye9TSELJ3Od4oT61ieQ5brKBocp Ymw4hhWeYyAIJVL1waBIBAK4Yjr0AUUe1gIipTiQjC92mCx7uDcpzvFattZYCE4kT/QClRIyoIxM c48DwJ2GQS81yqOmuCfKtniw2GEO5Q8a9F0mbCqkVF6k1BOmwhPQpUGf4w1qCskgIE7BYPnogG23 lFXjOBmejo6XSDxdLROwrJJaRoyulu0aANXa14KguDDMhIqTEFZ/C2YVOXw514qxgURGBEJ9/ygm 2LZL04oNhFm5GBjBAJImjenbXC3yOqiJy3Ne7bInyQ14muyHaQI0YMhpN9E1iLl5n/kKKkQZ7UXT Lu0LjOR6gQRVl6EpsqJU8UUyGsMrfON2a0pVCyMgLKI6Ri55opkLPiMExHQg6VR6aOhrEukD2uSM 9HCWUe3jLEEct6BWx3k2N2lMeo0IspA1mDV5FvmN50B0vYA7NiJRcoG+JoUpEK8sjoND/EDE4tkU xBUCLICm2YIAJkSoSfmHTvkaPLKhcZWcsyaimWYn1Q/IKuALqWUnx2hj39QpW2JFZ6J3ukWDSFAR vG2D6lIEMUk0HJVc7SSlVRq7OnULokKm6v/O6JoCFcC4K1bYVnIhF3j6KwbCK/D6OMTShxJ6diFR GgQwCXqNhBMRWc35NSuRL8GETouBnNVHJ3nijFAvR8+viOXngt11JhzVSDV3ndHAFXi3rdW4C6pi UkJguybFY4yjgPfawVyhrx1GtlthCrDyoIWnsA1bEG75PP/HTYugdiK7pZkBais7CbHlC6vJPlVv OysVh4z7EIACnBOIrbnAFNR2h0fEEbg1URKwaEvMDxSCtm3bVnDbFlw6vXcTujT1gI46G2Twg4vB GLsvI20QDbo1TPb7EMBmhaq2jYhgz4bsugtBN2N2rU0bDLqhn+Q2HuYBmeNOZ9fGN+oqd3//2nXn QiD6wnZFHA5sVw529ww2pWcLg2CDCLhXStH8Eh3jkT1KKPBiXJWJQNTYjnfyB+0wx3wqFHjxj7TV hru3wLvtIxykDSw2FTLa+t/qGyJsL0xwb4R3jxOKug0iQanj5Aik6Zz0a1vqLeGEoN7OicvTcRPM trSRomgnpTiAo1q79ckVJMqJoiKpfLh9IhajoFnHauDaDgmR4AAiQEvChwmJoAEiwJd3KAzH146M XAu8W4BZyugevBFJhM6r086LyO7Y9LGEbuHm2wvKUSfQfA/VEXjYEZAiPQtMAnvNGD6qdTo0HQxc fKX970wYnRgQbjKJbo9G3Qo4bdGG8S+N/3Eyk9GHojQqCqoVPKvBreBF2llfpiLYp83vKoVKyUMB oJ06bx0Pji1J1WgqnW0yo40jhbrD/W4OSl0nNHEPCwA21zHLsSFW2gHZohV4DgJWap2dFcVJ8n3L xqG7LLwRvz0PEA0D8J3RCn3XXycyMdXSFNAR5KFCDuK5VhoSyiQOA4wOQSieFe+T8V0n1Ic5z+k5 K80xCp4Wn3XkCU59LrT4nBNToW1ayffga8FjMkzKqIw5j+8AhzNgnNkVTARf9CAHPbDQFRzkgPDC hlB4EI0xw4TKHCkvhewCDhAf6H3azgrfAZB0bjl2uFODKi2gvJ3ThSdW/iIrA37D+J1cAv/mFr4b D/iP7b8+sXldyAzwwjwgAbeeFjgN2UbH4WV1Z6At2V8y3H8OcUbjAHpSy859LHHeDZUlu1YY6bxr zEAhF4o+RfcA+AwUDtWn503++MDS6R1k5YnCHBbt3Vcj3icTIWjxXXK9P7mq1zVswgwe7bnAFUSZ VmmFbn6/C1rXbFLL4kUMIvyOIcAh4AWv8A6PiP7QIvH7Et6kGnzb39r9Az79t0Jd1f8ekCgWt7VA S0HMz1lKeCZi3WNjL+jA0ql0t60UrDyS5n5rgrRa58iY4GoZCALCIbFoPCKTw0GjEwqBIIIptWq9 YrPaLbcLAHSxDI2FIJCQDYKQQKMQjMv/AoTFQpFQOSCHBoKRI2BgIFxZ4IUhJiouhhmEEDJGSk5W WTxNDChpbmoOTDxZUIqOUiFwPHU0cK6ybjY9cUCSzop+MTpgEEBYMGAI4K61KSjkmgrEEngcCiho tIXuEnAYJJtROarRam9XaSxzg0dahqi2mq82gIavW0k8fTycy88HPHw8fbPrT9kuWrxRUSABgzM2 bixAGMah2RQJyxi6YabBwT8FvKpICLVvYyIIHqxxDEmFwZNySBKgTJngQCYiLOkNSReCgUhaBDQ8 udASJk9OAy480QCy5rZ+ijC8IYBgoIIxwdyQcSiB4ZmHziI2QyMVoAACIGQRDeuVa9h9/15DxFOS YW2ItWsTFMkAt+cDKEPLLjJw6oPJnn5d3ZuGl5bRRMAgDGRAwEJBYRQF6JWGIJlVYRIjE0BKhc/g SREj/em8z0FbViGOFIArV0hqIgMS7NyUIYQD0YoMgAjx4cCmBE9+Z/hL78C9r7YpFTbsTamgQAic USDEZ1BXCxgo1J6S2UH0ORSYEaRJxUP2zpMVWHtDiAD6UjcVTO4KCYEs+lYYgLh7XBvOvppOC7Fa Ax+stQFcFWyQQQe8NaEgb5yk48x+XEgTwgaxJZFAcML5NcAGIXCg34RegDGiFgp4cJwGynBAUwga RMeBBLEcQ4EFHjTzBkN/XCdAHRT4ov8dCOKZqE1uGCoBYACr7RbAASEk0EAFQkgZwAeZJBDBKgNA UWQWOHWA5EkbugbUglR+0IGWAUzgRAWZTBBBBx9MIMQBH2bwICsevuglIsn52YYUtk0EGQdrqIGB GgZgwMB3AuCI1UEN0TGFBZAAGSgtT7SipFwaDmHgBRVEUGoHAWywQQR6cvKEplRAoBurmiSgZqkR HBjPAacmsEEBAyy4QAaZXBBPBhd62ACwDG5wDnEhDPoqFoCKZsAwCiAmVQh3SJDQMNnU9BkbbAQz RQgOTQGVjt4sI4EHGqwohQIggCvtJEeaNsSnZMqVAam3BsBEBR1csGWXr+IWwgKt1Hr/K64BXHDB Ai1VsHAABWCMcQIXaJmBxQtcIGVKF56zABT12stPiWVZKwEFGpzym8wz0/wbBzBOhTI3GtBkQGMC KAoZUhpF+gYfDGiEAXdTwAdptClLggE5+QYIV5gBf5DlmgV0nAmX6PT5qiVkrgJqEZ58OOVqQxCX wQQZdDyXhnK6lac8s2kEtco1GcAdTjW3tda/DjtcgVuAv4idzqOsiAYh5JoyIyF2YACCAg7ICG8b QEoB48sEoKE3JaSR/Z++cDWg6gZZF0BnBBvw9nYEF9TJyWzl+XlWAeaYTUQDuwObwATlRACyxXEu aXEDEywwpRBpnVOAXaILQC04SHsw/zOBEzywEkwHJPDA2/fI7AEFRDIOX3pUsAcSAgbER59SU7xf inqPUC/JWdDTynZLWR7gJQN4wAN2J4QFFG8VdcnPq0h3joY5LAARkMsCwpSADyxgQAOoQAWytIE3 KWgBC/jAr+CRpdrdjTbUsx4tkJYb4BTPgBwiQgEQOJvfgOAiovgMOGSUv0mQZGoznIdM0OcnS/iH E1wj3PP89aCNVYA3nshAATNQACpGbC4FMBz/zpGOvEGNhaIAXfZQUbEh+qR5TniCMkSEiPgwYhgO cMjL4GVHmL0IXtxywDB+GIZxJBGNmpAJGAN1ilkJEglrm+GTDiU6MepPAi/8QBQTaf+OA1SAfCCQ gBtJ0TLGIC6UiIuKAhb3w3FgwpJK8IQ67MUpVaplLkN01SNXNgsHvDAVYoJlJ14BBSOKAgF+eOHM 1hKn4qkkmSlBYATedsOZeQADEADLDymACovxcggVfMKjXKmkbIKTlnqDpCIyg4pAghMda8yFKFxY TO7B5i+vEd8zn5BDYNYEAdcyJRfw84RFqlJD9sRnoF6ZzmyKM4y2pESFQrCmg9IjArDo5BYsQswP FAuRgjzAAy5APij8Yx/YelnMRukNB1ATCwSwJioKKMgCPGCN26Kolw4JUVg2coUL1d8pzqSJA8gw AUFFEsaOMACNOssJIVKEA8oYgg7/TECWNxWeTMnDDUeVlGYJWstHZwaCPqS0CgawADGpiFRnPeCZ OeSnpizRRU48gFVxNQJKlIhOetQlSOPcKWgstMsiTKBgFwtB7XxzhFIdoXd2QmEr+KTXfjq1gzfN UAV+4wGCLsKdv/kgrqRqhNc0YIJdNR8/CYA5mWEUVzJUYpY8KjMOOICm3bGChLBQ24040BwcHIL0 VisExG7iAHVSLExup9NRKEA3vs3QB6jUgVNJcEOvQdJrhgCqeAaAuKxoXQjIolKp6SYCf53sEiJA PnZGgoy/gerE6FGABrg2KLi7ggGGqdW1EO5WBaIZCKTJ1irAsQrkwsKAN6I73jW3/4kHfJgE13SA BMbEpUetB+ywW4CzJkF6IaCpl8jZBUs8tFW8qUATdsexADQoFQ1GMYE20AGUbDVrAfjnPCRaSCsg 4IXiJe+eJAqFsG4BdJOcAIblATLLzhcLCPAbMUVpTxihtBt2pAAHfHETmL0BKoKg0YZT5CMinUsD uRDM0sAxtnN0wGIbUEUFOLaBOiG2CRN0nuHMi5LgrC6waanAW2UTghvby8NcwBcrMqAKEpLYSkAl 2Z1W3KQnoSQEvAFZdkvX2BB4GQuksVCReXyEOz0hyVqAQC7v6heukW8hitAnthwCL4d4C8jp6lxt YoEtiQijD3DwBRuok+k1vKFbEP+QAnXAkTBsrmICU5LeUQXrIUe3BHYH2NACuhccUKVOCCQ0h8no lT9Bb8GgCoxis0DWunrAzVRL7N2+hHBdS3eqwADOjfPOsUEnqMoIwi1CA1RRVJ5U1jhc8Nk1szkA 83KTw1lAVyIi4nD0oEFz6sI1G7iDNAEzTQOR+TU3YtWk7Tb3AVOiG1cfjCsyRdC61w4Ol2oIbyU8 Kx8KHUX2xqtvNdVpAHwp2AQdtm5+3dndK6cHlzg+nhDU+xwf3N2dGFvpItQVuAAHERdwqZs+q/In sPjvwmW+hYcLwxC4njhD2JAMCpCFXI46BmL0ASabF2EDC5B7PTqYkoOvqllC4N7/A9Z01HcLgcSJ 3pMTblvLUSDRHB8wUIA6EI/ejVxLVwue2QBf4z9r2kL0aADZdL67VV1AQ/BNJUquuJq0vmkeHxJ1 Q57gK/KO8MeMYDgiwH4QCfQiRGT/GUGs8OdmEMIjXB/jKUiGDgXZafLNQuyZgHXhq5HK8iC70p4+ tNQfgvtEym2FR4dQFwNugGOGXvHrRBv0p+/K1Bm+h3fTpTB6DH4IibYQrpCeAMM12PRZ6mBa52Ey w1PBOCTdZBXAhwhcItBeGDiAGizgL1DDsOlC30ggZNTGIZQZFUyFBGSDXmxEjsmKwaBQmzjIirUN X+xdB6TKawRH69QOJbHCsxzg/7fxFSNIjfEpkZ5UV0ysCmsYUJZoCEs8yIShmPoZ1Yc8loB90zkA 1IqFwO7UyhB0wBKtGNxgCT0kFAaWRBI8k+MJQRIKB5/EYBck4D48B1sZAHZwhF7oBhEiQWskVmxc mBHEIaogmxIMCIgMn6ZknxZUiE+hUZNcEIfsCoi4kbidQ/wFnioACLtpDQl+yJpZobzBQRZqoRZF YXYlEhgqXEN43To4AGYxzdOYxd/oBAFWkE8AxYtsoh7OICM0VIhxiLCsRaexgo9dHxacwnKxAue5 xrYtIpn4CmIhFksMwAjRor5RXRWchdMZwSLBzpI4CQdZCPB41AesyfAQTFpg0v8qGSECdqIfRYI7 XN1U7aAm2AM+gGMV7GGQgZeKeZorrBNFucMAmsMHZUIB1s4ivh8vCqOWVEDOXeIhwkJ5WILeqcW/ REwXZtf7KRubACRvHEsGQdcEMGMRPMlMIMIYpuMkmMI5vaMR+BKNbOTeaIM/PZWyfOTZ+NKQdMFZ sCES3Bv96YudtFlbMIgqXJB4mclL8ptdNJUyIMATdJq/lEqbwMVp9IrQOcnfvVjyaBtv+GESSJTR dZ0i9BEAsgMCdBMWfCMjkNo5wR0sMcEaRcFIqmMrToKQvUMlfSQmaRInIYLH1WFKckLslUczPAE9 HsEiwdeMPd3TDQjcNOXakEr/o22CzmGkGHblFaCLJLIDVWSBY6alJK3lMQ6RW9oTXJolFawjIqiX GbXXQRXjwFiWZibCOMAiXSqBj91YbuhiM8pS8/hl5QUH9aGKasxF02GdEdhYGGikFiCAB3hAUEac GVAZD60BBnAAkHiAFFyZUPwCB8DWGYjZdDINBzDGd0iKNW0lKeiCU0GVZfKEcFUVBKzi4bGDZv1T DFlSDU2QzNzTJLAU46lmhnzItlxBchmkJhBlMzUlUm4IqDje/XHhIj3Xa8rhwXDBb2pBYxICBUDA HHWFI5nL41ADCPiIjliAz6SLAQxEV2Ao0zCQBjzHupQLOFjUb1BSA4jnKhyA/5R8VA6132aS5D5g j/a4Tfe0qEWGz/hAkw610wtVAIJ+5BYNFFcSFjrcyu/81sWUw3tFo8RQGpPunWCtwj1wHYNWJbk4 xB84hAeAC7mIqQCEKJm23Rlki7kEhIS4molKZkmSFWrlKHY1VpT4KA4BKY1OC1oam98gjlsMTn5F gOGwBeBAWR4mwmIAx1y+o7D8hhxggTXtpiWFTCvMxoy2w2Jmarl0qbdAQJiqaTAslTSsnQCcD8MN GFWcT0Q4xZtygzBVTs10gOAI6qCuhUzBpzTJmp5yJp/qQ8uQlJOF0s3cQSmJ1N/oBpG9o3B9lGZo AU54Fk4dizlcqmIqQkYQAP+XTsVCcAYVjGkw9AIx0MREcAaqBgS0jAHo/IPm4A/fCARjNJmwQgEp ISqvdmZDVEEfiZWoLSartRodnQus7dNgjNVFkRiRDtF7ZRKech201qcidZe1JqoGHkIfeah5YgS+ ngHTTIV2QCAzAMQy9I0DYKwuTFNtMADr5ZMcSUXL4t638Cpy+KoWFJi+rilXSgKOeIl6PhWf0ekX hg9p4ikotoNDPexeRuyCamrMMu1xieGDvgEFZOsY4IED1EYgDEJW8Ew3VMfWIoKNaIoCvAzNEAip NEBdsQJKhJbhdFVQdOwixIpePuwTcJiWNu3domfV4cG5HMMa1IbSOIQBgGn/cM7LZICpt37ZYmxi jqUMtoCSKBFI3SiIk5FBQlBCUCaYEk1QsSAJlQ5BahoZpvnm0uJt6QaKh/mM2JJoKGirQ0hoxqUL V7CBu3yqIlwW9VgLYjDGisjru0RFQtRrF2QPo+obnSQAyNhg1cSFQsIffkqs6ULvXtXetkKAi3Ai rFUsVfAQudTX7X4toKWjPpGasYaEO7xcXPDPiWmMhhyvS2EipAVMaCEsDT3B8NntFczWs25BdFht 9PpvJAgaBaQIlZlB62rgR5SohGwvpBCC0iQCbjTthtWES3ZC5trJ8rkY59HJBPgim5TGm8nJ/AoB UIAvY5Iu/dCUq7qBAQTv///6r6CJrXekyxRYbf8Sw4Zq5RTkrzPQgTcsQoswrdeKhDtsW4ZY2mlM UICsSTP55WzqHdoOUv1m5AkLAxooZ20ogHR+h0GY6MtYwEJIRXVeLbz0nnbAi6q5cOneK17sAtO6 TFgU318Z5hI0F3CtDagAyGl4CEaxYcx5oyK4wYd6BaSYwYZysUQEAogKRJeCKNAEW23dGmSmcdOu McuUqT7k75fs75KpbH5SqEgkzLAkQRFTCc+tyR0XTB6zzQN80E/dA1Y2KBUH8iE8wm0dclYcwiyb K7lAJujY0STjbSWXBRCTYQp/XSkharaWhQcmLxG8TksQB1zYce1Uqirvyv8BWemnBcZ53i9tLbK5 cKADHvIYlCoYS4WaLhVkip0kA7O9zuyI+MFGBLIYM4MWP0UXk4E5W/F0PoeYGR4aEwUzIxUHcxXx nHKqJAjzzmoADMwIIsEd3uIUA/I3P0X1HsrsrqtQ8EysLLK5UkQW15Yh5N55trP06sM3BBh9qUFX OgJJR0IgWxmGfoSPOIJlAF9Md3RMOzJ1WsEd4IUHwkOGYNgcuoYWResSpCJ0LkI3V8EC6qsFYiwe mOySdUWEOvW1aCy2AIPHmmftlrQ770OBIeemuuoxdPIszHKF2rJNs0vstqya8rLhOQVe3MQ/7ShP 3CHfhiMVs4MhZDHRfjX/jQoa1q7Hy0CAdtJwBabBieLSoRB2KQhnUFLtFMSBNcSz21F0CITzAo4z zzyKPtPyMZgBO9d0Z3wl0olwT8wdG2Hq6O7HHLV2YIN1S05DNSAE0PyMQ/TCL/BaN6DHNEQGBu7t 3/JRMThSS2O2ufYBA1z0GWT0TTAAR791MHz0zVzBcFbLOIRA6AnSWGZmHLHsq7UsH9msbJt3Uczs R1sEfsCutjLDQPxM7L6uBJRHY3IiQiiENTgwO1y1xpKsGUj1sFG1LlittWD1xjJDhB6hj4giXhDD einrXzTPW9LUJ/GuvEITvZ73hkuCh2mFQ6BIe18vUrSqb893fe8tJ0ZF/+DS8IKnjF8Tc1O7OF6c ITF1AInddWuVD8ZmgUBoQLy+g1scU345Uwa07ZO9LYcr+RagbohkhthKAWMwMGU0ymLEtzBIAwvf on1XxWMEd1dIcP7AtpJd8n7wbFtwTPcoE0qUyrFAUyaLFQQga5DDU2rLYY8a+cz0QQsveRrDcHg0 xHU4QzMgBEo1xyDcFmc8dimQqIT073SAxX7rKb0YOMweh0DEKobbjAU0IBZ4qFNZyPDYuTm81wTc Jxt5dZ8reSWzs0hgDjjqk6vhkbDeDLs0jVi02u7ekR3pdmzDwZyHzKj3xHulYlAAtqq7cCXncFlk K5/TNaaDOuBIbj0BTv+VTYVLd0ZTAQdKkhcTPJNVIbtsC/MyKwQGuGysTQhW3VeplN4qpIbWuPnM LOexdwYDlBGdCLsqFQAHsxG9h/vdjnsHHvaPa/pXQeiuhoNpgddmDc9R84SdnvoTKA22/+rfWKOY vMZdfyHCvYiz//tIBnw41Femy8xW1ep+eZV/iZR2PxXzhGWHLECbyExIHYdJptIRBKaLtaiPycxa QB28KRYr/dLH+/k71wQfoBbHCFUrpMbsdFWhgIO2o0I5TtaDVdVZb8R8npXOtQQr15jfzYp2/aVL 3Gd3Er0aG72BUabrzZVfcNSpbxLFa9q9s2VKYiamYf06oBKt7KeW9Bv/lahCnMwJ6ALXvnmw4wXH tD3Vwoi9B2Pe2UNvyJOCvU99vrs7x3svJaDIO+zY0R4c+ehsTQASJ6Bg8bQEcCHWWgxA6ywXcGEb siQ03RHH2INkK0F+MKc9O7CUCfJSXpt9ou5+5ydBDnY7x0ttSMSKEB2myM2JKqB+x1jMEq7Y00kM lVxbdpkM7dc+tNw+7tsGKmHIdLmExn/WJzz+InQk0tncTxDIrGaC1JXN+e5JZYEIws+CIyi/Jvxb AJwiEEQigYAwkEkQkURmcRhIZI5JqLTSuURC1WaX2AiFDAJy2XxGp9Vrdtv9hsflc3pdDQDY9WlK 6LPwggqZYBoIkQpM/1RkWvgIoZhDAPGjWgyYuBggqpAqKLD0igIdhXIEQdiD0wi5IA14qCjcMgqo GFqa8qIVnWj4yjjYIDLksrwI0UhVXmZudn6Ww4OODKvsSvjoYGroQAwosB5I0Bwet0wIG4OTDNkg Bw15Hxhq8O3tGM9gPThikhK91CFEBU33rFkasCHEqWllDPh5B6rAhwgJElwgtGBDggcUc31ssqtT hwWNMkwseeHDAYCLBjhS11DmTJo1l0mzucZCiCeBomzgFwCjlIQbMnT4xO0oP6UdgirSYmHdpFik EgjTdWvDggEZHrxqtYXIFlELMmi68DXD1oijKixE1bAPIVffJmS44P+LSIQMFZM0+BQAcCgqBfQe uFBhga8FiQ8IMTxqwqOclS1frowTc5lJgX16JfRSVIOqE4Z80JTgdOqeiQqE8ACHA6u6LUPeAlQA K5QAYntz8QQuyxFAdZkc4yBz1UHjzZ07R5ds83Tq1elonh5mUZQC2kgDPNAgwoYhG8gHNR/h6aIw bySE6NDWUvcuEebdSmL791guBz5kuAu/5wYQSIKGtHsuQQXras86Bx+EkAzsNvMgBM9CkQKoCxYo q4MIFrAlgAFIw0JEEltZ5LXY2iBgEuZAwWcbbYxYgkAiCgjrRrKk2JAI00BqDh0QCJgGwQWPRNKL BiNkssnM8qhup9b/rpEClg+4wCXEs0TcYktiFonKDQcOca6RBhJo4IMkaKQigwqiKO+BKHas5c3x CMLlOX0cKNK3JP88ckknByX0mQkxeyiEF4EbiIvx+LrgpAAxuqQvShVBRww3MAhBryA5mSAwiwQL bB6viEDsgse+8WWAux4o4KTBEgQDg2mWAzTXBKMrtFdfUzkUsz7+CGSAoA7QxFgiFlBvHk2YLS4A aBdphDI3JpFPV21HeQ2EaeZaUDUhhEhigLzM9XRbLyaD5Fd3330jWMx2GiRbdV0NQ6o3jFS3X3hC mOYh1BTka9yKiriggAgSHoWWBV/SFF6JJzZDXmHD6CDdftMMo919//30N+RABHVmFRSfc3iYCio4 YOVPRozAM4UBGcDlI4+RjmKd4bUYMwYqhC/mbRUWCDYG5JhtPZGXDuCAEJILOAyN60q56Q46mODq BhIyjdgDsI7064wXBCPinc/2tWfMCJBgkjA2eEDpBA94QKEwQJCASDl2+oppvx8IQd9pIJAa5TAO X3MIIx7oGzGhqMik6ubKhgBty3tVezoHVjn8gywSuFAi1S4oOgwN+KyDAfgWVBivB+QbNSSRBTpa JnqnbnhKJ3ZfKwPfrwRZ8rrKFvxy45nMnDoDIMDA7cPb8d1ggyO1+3kQMIAgJjsq7Ns5/yZIoDF3 6psSEZABBXzFmf/opYtq3Y0wIi2LRr0S1fsSnCzw4/dHHkpfEYAABTTgvOcV0HoaoAAE4rIMBfhB bqQ41XGGYCzDCOExQUmC08olntDNLQwKsEkf2vFAqLxPcUN4AIoSEIu0fAM1wgNFMDrGPxo+KHlO QoACFAABCfTQhxBQXe0aspOVNOclXQgGFK7WtSwQawuTyZBpkHIk/+gvJwxw2wTspYsCSgF+E+zd +L6WgQ/4ghu4UwS+FiLEGrZxMzecmAVsJRMCzKaItfEGE8gyML4Q4Sr7IQtWYjc3R3BAbzkxAOco skXvKc0cqOpgIubhCGRoz42XfFIbWwRCOtoxWqNIYhOOCBCHbUH/LFtIiOfQ6IpqGXIzPwvDB0Ll N4lMgJIeYCMmdWkTOE4MAlDrZBi06IoPXKgBrSBlT4DHH1TVrSpGzJ8rqeMAoB1ia7Tswoj0EQYP oG6X3+Sl/2rIgcrRRIRja9j4mqamYoyHCLAApNWWdbLhFc1j1mEA58KQl0iqyzDHOJwGcglOgjak lxNTwJBqogCg5WkRtvydXki5gW5MUSzdqEVFSYipbXqAkxEygASq2Y5e9PNIhplA9WAjAUsW1KXQ OOjEMFA8Or7nbatsQgI2KiLmiONGi1JEA6qXt0IBUJ+xBJCcTDofjtyFkgHN3kulOpOYSswADLGJ Aejlhwns1G8H/7Dl4SzQ0kIpQAIDNKAffAcg6RlsrU89oAQ+OlW6TqOqEjurZULqvA10FZuoGs/h 8HZIihnArBbQwEjTuljYaMACciVrXSXbjLvCiwDd9BmnOleBWfXLMFd4HgYGajwC6HCHZ9WAD3vo ANNO1rU5qawaHMAngO2BAjnMmR5+RtjKEMABzXvefz4EVOMcgFlktB4GHMBbTPbwtc99oziVQQAL WKC0AkBAaYmkgEMqICaGNYMByKkADVyXDNqdQ2qtY1a0FvA/WYiAnOY33/mKZ2FHMSAIUjtXgjoX uv+FrXRTkUgNPEQAiRUpBigQGwIgEHsCYICCc8ZQC1CYAslBAP8HzsrfNjwksphBAAPOOhvGltiA HEgtAz4MTv/qwUBqMMAYXiwTBxiWwwAmVGzT4FyACfTAR9PADlGXHAwYKLtlCLICoBZkDIzBAHOM gwAJZVgRS0CAGsBylrWMwB7m856ubbEdartjA425IUEOM44LpWM08PjAIAzymzWA4gEiAAEW8IB1 kaxD6QQZGVj2lhw2ScOHLBDMMz4DdVNLgDuftXYQEKiZEYABDNjZAx5AQAjy+eJJV1oADoCABeKi 6KNR4KwSyGc584kBOJsV0WrOsYBT4eY411oBFqjdcl/82D2TlwxB9oDeyikHatZQAsA8tBoSKAAL QCCh2fWAARz/IBXClaGOMTYkj/mk3Gtflm241BuuqdtgqXCAApc1gLev+uY0w9pJbD4DpA1s6zeL VwLVFQAFihztMszU12/e9OnqoOFxDnuy7T6viDX8byZzcswOeLEEIF5mMqy2wreushlEGlV6xxmA fWD3q93dJHifgbsgPHLK9aaABRqWsNqNy5FLu2IYmxUEp1VtzllrWuY6KaE076/Ify3XHjL81g4v A8QrPnEB1NaHqS16mpeHy47rkAMq7rGrR75mWaNNAVXGsmJNXGIPYLnoN6aOlJOdhiHZ2+gRFkC1 z8sBbLON4gLooXgJQABWhxnTAlBu1QMY96wjfOs27Dq8dihA/wIa0Ci+s0VbpccJ36k0vwh0dnUu 6826Gj6fotYAAtp1WwinNredRgUCQi+d2QpAARjwcevLcGf1kt722UWsiB1wW9kfnuSJL2qoSdzF vviFkXURh7h8l1YONNvQOUloz11qeN9Xvw0lr8nygPu8DdgCdNgERwQqYPnr1bgylD640K2//jsA /0GiH6nnDvbX7SwMruZ+/jRaNNqCUp/9/5cQ91OeBXser/Aq+gsEutkmbmKpmditzlM/AARA7GuG zXmec0HAhzmm5xG4M/uy6YtAk1uuqFoDRlMGabMDEzQ/CbQMCkwF36qmDLimDPwTbToczIKGq0K7 b/I/MwgBBP+4N+kjg3/bAyKcA1+LMxbMpAehpliaJRocmrCCDc5jhl+iK+o7tXxDhkvDPR8rPevi ABDgkyy0ttzLt9SDBNQjL0czg0nrwM87pDDcHObRM9RTQrsSwIUCGg85vi64lOfwK+PwBMHAqTSK gFvaQTsgOKkyPOcaPIBxrjgTrd8igFDztd3Du48SN+uKM/IygGhDAI86BXQrAw7ILlMULwgbNiSk NjBMt2C7Q0PJQzoSIY8oLoHoQ0VwKFIwgkEyokPsGCGkg0zLPx5UP4+yuqbDO5biAB0KoAorA19L KNIrg40bg048nRkzOoeAuJtrEVwzAyQEIfKaNh0Cx1ikrFn/nIYME6Zc9AJbgBsmQIw3QZXEoIKW kUElKJcA0QTDWICM4ARfiBUkiJ3GYBlWaQAAYaSaCQNTbIa8einDCwHVUsai8wAf+i0QYrR/8y0E Ci8IoLpx1AAeGsJtFIDNUz1OYgALACZxdD3T86FERMc5cME4YIcYeY5iqpsbyZhG8ISeLKbu4JB4 XAK4WSFk+o8G+JqhBAzfERdp2QpuAIdBgBNQSACBwKpl8ACDYzH1swA+8TVINBCHXC1b4SFfa7a4 E5y/U660hL1PZLQg6zNOyjDXu7nfwi71cUlPNCS+k8mZjIOafAPVOQR3DASh+gYLuQS9WACwYkyw Ko6umIJ//2QCYbhKP6KCH/miAACKdwIfbSgGhNimv4SDnwNBNWAbxyKSZGg9rVKvT1s0vlsuAdIz MqA9A3ky5YKE1xsr0SMDasS7FIMESPO089JNNHQ92OM/wLwOdWwGdngmPekGfSAEh7LOApoCLXge i0AEc+kAijqh3fGNKAAI/ViEt8jKVFC7oGPO/xNMNrisRlGQ15ifB9AGxViWFSoODsFPVJmCBmgf fgCIENmdzZwiwXgTRDDP84QNYYyDy1rONurB9sSx91yDPtiNBFmYJlAToRqAiTAMdwBRD+Ud0Cki UQCIFrrK8IQfgtAN7vSjPBoFhQhBOcAiB+WfCaXQ/7LQNP9IlKUiBXpkgvgqgmzQi0NEp0OUJR/h hwUQiExoGrqQoQtAB5agiHrwESONUlRpH1J4jRDAUTiYKfbc0errUTQgnOiEwjUNhLfgSj0YtBoq ra97OqiTKx0K0zKVqjM9A1xh0z/1ggVABma4s63MOQlwNu96l8VLrLEzoLJLINLU013iUx88H0AF 1IWwA2k7K7EjuxQDut5igAtLq//AC8m7L+Q6MQqI0EnFpEotA37BVEwlGRaZNrGbTtOQnrvArwLK s+WaDt/SrMPpvoo4QC9gCfGzPG5zVYKCVTKYhFmV1t4INDEZVrX6kGOVx+OCK+WyjNd7HqzhCkAZ gH9UKVb/a1ZKdU5l8NN+WQwvqCBtRVbDDJdBZYO9Ilb1SJLHqB68CdU9aMK3gZWQKYC6uUEqTFf+ eVbCU1Nd8Q+NSRPTWAt61cd+8Bc3LcGt8hAgTRCiEas8nQNY8oODpKWWuaVWTVidWVgCCAOONQ6f itEuANHjiM6gAAd48Jcvlb62CYMM+CR33Sa8cYZEiiX7eCht9StkcYVJMp1/TVl3WVi8awdASRMy 4oeeDYkuVZarMIqiOIoCcNJhiAck2Kaw5RKKXQQaTQN2bAfi2paraMhipAMHcBujtYRdDKpPwFuE 0E4xfFrjidr4bNjn6A5N+JrQJAIqRZX5EYS/KI3TYIpY/1gCsSiiY/qTt4DFM6BbP+iea5DXBOmI hUDYOaCXk4CgNRlShFRIUrnKCviExlBcwWiZB4qVfPlby4la7KIKJHmA9gEK/cAFXqUTVBEP8qgF QtiKXBCLCiCEvEgS9Mw/EdqSdTmEDSgjL9hFsdCdmC2WbfrAOKCX7dXFJPANshiIFZICguwA19WI 8Cmio3jCQNBOmrpdicld19sntCUff4DRJpiAziUGgHDSDwmRr6EP5fUjd6ifhxlNNGCfRBgPcvCP g9hFKrhUxKVeKyJdPyhE7CVfPVIiJkCKJShKcmCWI+hgjqHf+oXadX3OScDJ5wilUZLRq3wHLSiG LHkCrP+hi8kVYfE7kquECzQtnEQopiaw3AZ4gL4AEOvt4UsgkwPQB5LAYC+gnDl4jzuqCx/mj5Yg 2ySY3AIEEkWoohpl4Xdz4ecksWF6Dk6IgLExzyuQ2KNoJ/LAC9MFnMBYAlu0JbdFiGjKvwbqFDLO UBG5kkNsSndICF/YAg3iTEDwjyq24g+yySLOnYoViwD2hg2IFTBOgvgYBr314y8IA7k940G5X2ur RfEdBWYJCmVBVgtqGhF5Cld2Fp6SR9bwI9BEGUo6NzQQ3O2Q0d+IgB7ezxzZj/wQVEl+xwZVhUEY nlaYWaeoBfMFhITMhSVYGRFR3L1NhMnIrVPGnDR+Bob/wpjXmdZA+JFfLBqPUoP3AOU0WmBUEQZa wAVROKVNwAIcXlAvIJCJfINMG5i6mAx0SpMy+gejOAR+8CvAGYe3QKdAHAWIMWVxjpBURoPN5SqX pUG8oNgCkEK/XQMXAYUIStzwJI4vIIR8nuHhtUpNdQNwyZV+BhR2sei0IWf9C1hr0l9ptUFuAtY1 GJNCTgT/8IsLGB97JgmfBCQTTYmVoGkvEIjR7VNF0ZWoThJeuWmucxILPBwMTGeX2MCAouoz4Bsv hRR0hgIqaAAQid0nWGJpcQzI6GAmAJwVPgNZTRJY9pda3eqLzmmaMAACPBwDDOsmUMDn8QAKcNrZ GOU1/0UHZFMDvT7sLvDrv0a8/yHsWPqcWR0duFrsip7sC57Wy7bUymYPM8NswH4X7Wu8Yv0+Wgq/ 8Sug6yHBOqDsdDZtJLNqwqWvwJATaanr59Dq1e4figEglkyr6DG+vbaIB7gv5nO+Zcjt0lZtPoBm lJlO3/GFutGp642hLiUFmzbu4/a6AGqvxXo8N0FVg+HV5WMs/YpUaEga1BYEyV5biEAZEwpNcYiI AxCVYUYIRxDt8r4MjG4IOkUtT3XURzU7VJPUPTjrVo6U+CUbjn4FDWaDVRBvV6iaTNFOKWgKvbgC o+gNMnEFcDZw894lG9OhQ825RMVT6lAdog4EjeCQQ//E8EXw5kBQiLJuQ0ummu0Ght0RBd0wXGGw XOLA6i4omwJf8SUsb5I2hmipgK8YhweYQWmZv29gnHfgoB6/Bph2DwdqDvGbL03oxSopvjfGEWto cnl0BDOOcik3bng+PptpgqBB6k3Igr6ymmI+4pTiixh2iQLZGz/4WVCQnDUvgjaPGYeKc8FwBLyu 8+ha8WBOEX3wHAtuk8ZEkYQQiqD48oExhFHGXJAlg/B1n6zggpaIBXs+EwHnIg2/dOtA8MMT5LpO AFu62iEVgu1eiUOoPCr1BjEn5RCIcDMoXY5+47UCECNHhA3IgnyciAkYP6vBqdq19Vuvjlw/PMIZ 5ET/yKMf8Y34goU0V5P5OQAp5l9LuGI70Gi7TRH64odB5GvxeIoB0HJywNJi6Vsg9/YDD+yEfWAf 7558DAGaQYqvSRZhaKEi8AVqdmRFyB9LhwOi9QN6/yumraSBZ+1Ll175+BqjwJqxMPknyJqlsJq1 qIoxuppF6YoZWoaA/QCS/aoKuCWBB3mC9/bNBW8keqTfiO2fuoYLgdlE4BiRrsBqgpsdJ1yDBeqe /72BZ1tkJ+1d2SaHnAZwJdYJGNcaNNfQWnaqD7Ce59lDWPTU/ROzuBs6f8HfKiDY/tyfUtYCYlaz R2Oq16rD2diheeOPtQwCGNXhCy7fga+2orzSeR5z72MAVdd7nzf7weYrfUUSfhWsBqwORmXwT53v yP8VcL9Due+cvmjMujAuvuhWnp8OG5u4Q2WAGQf9iRH9WPQtPDOgXJU832F8bvpKyJ99dKx9wOTU Rm3wxpI4pw1+Ch3+Ms0hV4txHYLy5U/X5qf+65/Agsf+7Wdh6+f+7x857wf/8Qcw8Sf/83ct80f/ 9Z8q9Wf/93dW7Yf/+c9++rf/lHX/+9f/48l/IBAIh8Si8YhMKpfMpvMJjUqn1Kr1is1qt9xuFADw isfksvmMTqvX7LYbDI/L5/S6/Y7P6/f8vv8PGCg4SFhoeIiYqLjICBgEADs= ------=_NextPart_000_005C_01C33286.DE8EC1D0 Content-Type: image/gif Content-Transfer-Encoding: base64 Content-Location: http://hyperphysics.phy-astr.gsu.edu/hbase/images/gravf.gif R0lGODlhAAI2APcAAP/////jx6+ciYByZL+qlRAODAAAAJ+OfDArJUA5Mu/VuyAcGc+4onBjV1BH Po+AcGBVS9/HrgAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAACH5BAEAAAAALAAAAAAAAjYA Bwj9AAEEGEiwoMGDCBMqXMiwocOHECNKnEixosWLGDNq3Mixo8ePICEKDEmypMmTKFOqXMmypcuX EUfCnEmzps2bOHPq3PlQJs+fQIMKHUq06EqfRpMqXcq0qVOYSJ9KnUq1qlWpUa+mFDBgAAGtYMOK pZp17EcBBf6p/VfggNm3cOPiLCsX44F/CAQMFJDgn9u6gAML9kh3cEQFBRYoKKgAQQHDkCNLXlh4 8sIB//Qa5MtgYIMGAhD8WyCAgQO2DRx+Dj269OkCqS3Lnm2zMm2DfRsmKNCWgOMCXhv8e6Cb9wHf vIMPv828OUrbzv8l0P2vcwAB/yAQXDCdYV/r2P21D+TuvLz5jtCbSy+4Vu2AgQkQECTw7yv87gvj z69PMAH+8wAGGJOAB603HwEI/vNeAP7tZx+D/yXU4ED0PTghgW8pYB1BEUSA4UbpMZfbQQooeJ+D /f33YEEXVpjih28dECEEC7qEIEo3zvWSAgj22KOHRD3g10F3LdgifycOFME/CB1pYXc5wlgVAw8U gB8BwtW40gFWLrDAhh9xmYCXYM4Uokf0tbeWlkEhplhBEaRl5JVIQhhABAeI1iSdT4pJppRUNTAm fv4B19KS9jkQIUeIDqToTWd2RN8DPiIIJFHYAYfgAAUggMCcKJ4oo54HOdnfAkg+CihVA0SY/QCb KD0gH4VMgiTrfpC+5OJTEUCAqnRuPfDXZwQxkMCGxNKKULIBGIvsArMGQN9VXHklYKu4wXpQlByu GFEEGx6wQEIECMDjYhOBS5C4udpY52TTphvuuFSh1V5bGxHwmgOXbrsvkIL6J/CFFj2w6AOoLkBc QTISjC2L2hqklmYEYZYRWhE7QOm7FGHcbku7WhavRR5Liu6WeGnG15AY0edAuV6eXJDLML8Z8MBs YaQAeQVh5pXPM3el5cP9RcweWzJbbFEEp0VcYgQhp9u0ju4iMHACf7XEY6UIllnSyFKb6BHHJ7kp c2OPYcSztCwbtDZ9WTNcnUUHQJDWfyX+1oiZzAgRDZ/RBOH1T2wDKU0RA1b2a1CebHsLEeIJKE5T pBzRZ/XAca+UppoG4ljrRJBLrhHZJmFGMUGcXYQdmNZuNnfFjsepLQSRD6SAA+IZFLCVBQl5cokL K+Q3g4APpOBpDxpekLEE2J2dAgOgikBnCxSvceO2O+DAYgo474CxmVe/E+X5km4Y2BGJT/dfAiwc wXuZCdrAyQZjreQApnUmgKID8E1dSJwKAI+8VrHHDFAh+kEIfbojHMex6D8NoNd2CJeQA1AwAA3I HEIUhJhoKW8/BXiZkKAlAAEsoAAEWEClSPQPD7mIAZ7qDNqOwymxUUiFPvoYS6ImGWP9USSFK5QI wgYimsUMwAEBGM1xEoBEBuUlNO+hzwIa8L7eqAoinXPI1rjmNUUJRy2kQYgX1xLGxZkPg5mhzwVL 9R+C2QkkJhLSgj5IqyYGQDRAugvtrkakWVUIcQhA1102BLR1XW1RLyGfRnioEQaIjiHvE5okNbiT hg0sXf9QAGISoBf7LYdtzSoAugjwmF2h0HYFIKBCsqgmWG1OTYvqCwK+wrTXsQgvtDxNmdaGkJ0l 5k35aaOrEDk6IxXAQ3RkG8VMxRAa0apKwAyAr+Bkw6AoMiOMzMirpEXJhBjrkAlYo1hIs78BpKaF SbTPtBAmyerEiwEKEprCIpJFH/1VcyJ9eRBictefOu1TbqdToFociBthFjQkYovTdJIZMmYuJJW0 WsuTJFY8HWrujBZxZACGxxFwevSjIA2pSP2jSoZ8ZgCUmuWskDSt6ElyAFCrFX1eSlAJfY4x95TI aQ5qkJ0+sCAIkKBCsJMZ3UBQqAGYIkL15heG1smhCTHhfqbXqRexp6K1eYmzCKIA+THgPe/LXwAO 4MXFCCBrBCDOcQgwpgGcdT7BswjX5krXutr1rnT1n0NCc6wkQiA2LGWSVG0H03g9jSCUioiQNFik g0TypQPQ4AcRYMeK3fSOdlySOBljJcfo9aeIzSRXP/mRajpGOAKdKK1qOpC//aKokAEcLVZrck2P UJYA4mKSFKnIJQHoazpcIgjuiMfW6gXXUfykDW/g87rACtBQ3ZPPyJi4mCo9MiFmg5OcDvLNQ64R nsED70AYYB/xjpe0QgpoqaoDT2Ja1XY23NtSl7eW1L43mwWB6GrHg86QyZEoteUIWtBlsV1lUFmI 0UuJOrNNbJVIwUXNCbdgkiwZ9cc6PmzWaf7Br2bhp3tpmeVEMuUVAnDKU7NFoIJwmxh0jYhBK+ZS NPvy2YH8d6Ok3ZNBfGbinHLknl+0b5KwN1Sh7mqBjuoNZnw8PpsQbVpg+2oEawUB7bCLeBvtznCP exM/fek2vfqV/YSls+j9saXDnvmwmUPYr+Eq5HZ2hHONmVWxhKWYIvZjzBWX11fPEG6rCqkynwmZ APuYOS9M1kmAN/Jk3X6uAbB5gJD28pjrYflhaJHmZl3SqADseVWgJkqJuqlom5ASdY4mSAFU9jnS iPbS+Fm1fm1yK2WF+taVtCVmrpuTRW8EAdqJgJ5GNk8YPnoBdmxwtCAQ1JyoayBXxrW0b3LaVrVN KL7WSAT6sgAIMCnD0kLVsXi27QcdGHG1wk5cc1Kyabt7Jgp4gNBYW+qa8Ah1SM3Iknh9Ehnd7nO1 vPO7By6bbGNkSW4RtsAbMoDktgQzQe1O6AhOcQIZHCN88c/CvVO7mXNghp/qq7jIz3Nx88j3hkEc ucpnU/LyKM+SAlu5zC3Tcuckc+Y4p7nMb57znhum5s3huc+HXhegM0foRE+6WYx+Gwsr/elFh7rU p04Wqlv96klhOta3znWLaL3rYA87Q74u9rKbPQBkP7vauZ72tbud6gEBACH+HWNsaXAyZ2lmIDAu Ny4yIGJ5IFl2ZXMgUGlndWV0ADs= ------=_NextPart_000_005C_01C33286.DE8EC1D0 Content-Type: image/gif Content-Transfer-Encoding: base64 Content-Location: http://hyperphysics.phy-astr.gsu.edu/hbase/images/gun.gif R0lGODlh/gE6APcAAP/jxyAcGUA5Mr+qle/Vu3BjV1BHPgAAABAODIByZDArJd/Hrs+4omBVS5+O fK+ciY+AcAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAACH5BAEAAAAALAAAAAD+AToA Bwj9AAEIHEiwoMGDCBMqXMiwocOHECNKnEixosWLGDNq3Mixo8ePIEOKHEmypMmTKFOqXMmypcuX MGPKnEmzps2bOHPq3Mmzp8+fQIMKHUq0qNGjSJMqXcq0qdOnUKNKnUq1qtWrWLNq3eoxgIABBJgW MBCWq9mzaBcO+IcgQVmR/+L+ExBRLl2Ya/8JFKBAwYK0gAOfZeBVAAIFchMrXsy4sePHjBEgEEC5 suXLmDNXTsC5s+fPnRsE+Mc5AOK2bgWrXj11wT8H/x44QKygcgPPAW6DbiDg34DfwIMLH05cuO8C AUIrKM68+APQ0D+LJg06wADW2LMrfRDXgQEFD/0Ufj04oLfm8+gxz1UwmXLu5vDjw4eAmPhygQUg 69/Pv7///wAGKOCABBY44F0CJfAYgto11FsADgTwFkLjGVSeXiDpVd5ACRSW3ocgYsbeXJYd5ht+ AiSQIAIFCDRAAg4ItMAADDRo440pLYDAPxAYAIFBBBRQmZDXWdhbSBoiyBlLFxb0lXUILVAjAC/G CIADAhggEH1aArDAkgAQABaOZJYJEQSS0VUhQQYY8BsElBVZUJMZUnkXAQ00IN+efL5ZX3AK0Ccn RTS6CCYDRwKA6F1f/hjmhGZupWKkBxEAgVflxWiAlQQJEJ6daxJEJ0UMAAcBaL7Rl0BvtYXo/aqr iJGI2aAhiVnklw0IxEBculImowO0UtoUhsLq2sBkRRaQK5YGwWZXqAONWtCMwHUmJF9xtSeAbp7J hUADD0Ca0qI92SqjAXflZeyk5hYLFLGREjDbPwX8NZCOBBAA4UIVCgcnaZUpZlkBnQHnIGUtuquQ pZOSS2VtMsKocE3wkklAApM5wKJBtyl6mIiMeYgwvQ/8Ju7ELbXLQAJdqquoAewWivJIFdt4MQJu rgipjn/ZOtzK0ZU8AGwzF8WwQA/4CkDSjAJbNEY1GwQmVdT+JvVk9spImkHhJqQxwdBVtunTTVGr K7oCwaaArgk4SrZCURc09VMvGpAmZaf++XgptAId+xYDDnhmQMK6/jPl24JN+eKkEPwTANISe3my sHETYB7BTRHwgJD/KFCAA1kPBLgB4CbkmorzJmctgykiTunKVsJ2lwMNWCmlmXHn6fGkR2leAGIC FNA1RoYdBluu0ar+QAMKTO66sAtAEPtkaY/tZeiBxY1AWR0TtYADv8+VQLAW3ez4j3MR9EBb5jn/ PNnfTz977TK679TKYel18eEAEDt3T9+bTorIhxGNxUVPCBhAABAwEAIESiD7ihTv3peRL1mpcXd5 DqeggoAAcOcBCyyIX/o2wZwEcDQDDIkC2UIwAUDgUkNzEcQAkIC1USpuFOyIBgViAHr9QQ57RMlP YgiHtOU0roQ0OSHOxjeSC6EmY8lhHss6OKkBIACIOMJhDkVSFtpZiS9WKhUWceKaxAAxacIjYEsY AAHRTGYu9qtgA9gCI0yFKUsAOBXoooWADeJuizMZgL2E5ChlFSmOLOlNXBi0E40FwEc1ahNJghSX egnAg0jDWb4GcKprLdCPfwSkTthYJMQw7gFjTImzXvMTT4lqe1zEGLoSwIBvhYUAdguXgrLEGYMp TIui1MmqppQle6XyIkgcyI4Y2MpP7SWZG4nQeBCAKEetzwAMmGMDjlksYAazJ0Oz146KBIExHYR/ DMGheYCirHsx8yMKxKRA9EI6LP0h4AFo2ubzvImdvMQlgmbhTY1wmYCsYaxeDcGhgqBJxn/Ya0Me KQ9AIUijNgHrkmqcGT9ZA1EvwRIw8qriYUYzF1AWBIcfDIru7NSRBRwrNQVB03Wy2ZYtbnQ1HQUA 3wIzI+54K0WoNAgOCfAPRCbRoSzVCJ7o5Tw0sUWfNk2QgaZK1aoqZoIDWM6b3kklq3r1q1P9Cidr BC8FOYaROdFdTityM6h+M53CsmJlTGMjn2YLqGUZQANaFBsmWmgotVxalyyCpp2+FSE3VU1H9YVO 1ehrkSYlyHESdqqM9mQ5/4tIhO5z2IckVjA5NSxgDsrNec6pbfgpqFC+klmH10g0sp1NCEMbFFrL DgYiWtycldpW2piwdrYIQRQC3BbbHH5PVM6c2E17RM7GzuS3EHFpW4xa3Ore6LMDEc1AnesS6DaE kg2grnXHqx20SqSWj5sJZoEbJoy5lbzwrS53WaIXAcA2bciKr3736xLX6FSNm7UtfwdM4I1saKev LbCCFwySNv53ToYhLoMnTOGKNAB9WZMuTCvM4Q4/ZDwYcuk/wuvhEpsYbvkqqnt7e+IWT7ioVsSa i2c84wAUIL80zvGJ9SpgHfv4x0AOspCHTOQiG/nIMwkIACH+HWNsaXAyZ2lmIDAuNy4yIGJ5IFl2 ZXMgUGlndWV0ADs= ------=_NextPart_000_005C_01C33286.DE8EC1D0--