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ꢁꢌꢆꢃꢁꢂJꢂꢊꢐꢎ=ꢋꢅꢂFRORUOHVVꢂFU\VWDOVꢅꢂPSꢂꢃꢁꢐ±ꢃꢁꢑ&ꢂ ꢈꢂKꢂDWꢂURRPꢂWHPSHUDWXUHꢌꢂ7KHꢂPL[WXUHꢂZDVꢂSRXUHGꢂLQWRꢂ
ꢊIURPꢂEHQ]HQH±KH[DQHꢅꢂꢃꢓꢃꢋꢌꢂ,5ꢂVSHFWUXPꢅꢂ ꢅꢂFP ꢓꢂ ꢃꢀꢂPOꢂRIꢂZDWHUꢂDQGꢂWUHDWHGꢂZLWKꢂFKORURIRUPꢂꢊꢈîꢃꢁꢂPOꢋꢅꢂ
ꢃꢎꢆꢀꢂꢊ& 1ꢋꢍꢂꢃꢀꢈꢁꢅꢂꢃꢄꢄꢁꢅꢂꢃꢈꢏꢀꢂꢊS\UD]ROHꢋꢌꢂ +ꢂ105ꢂ WKHꢂ H[WUDFWꢂ ZDVꢂ GULHGꢂ RYHUꢂ VRGLXPꢂ VXOIDWHꢅꢂ DQGꢂ WKHꢂ
VSHFWUXPꢂꢊDFHWRQHꢇG ꢋꢅꢂ ꢅꢂSSPꢓꢂꢃꢌꢄꢐꢂWꢂꢊꢎ+ꢅꢂ&+ &+ ꢅꢀꢀ VROYHQWꢂ ZDVꢂ UHPRYHGꢂ WRꢂ REWDLQꢂ ꢁꢌꢈꢁꢎꢂ Jꢂ ꢊꢑꢎ=ꢋꢂ RIꢂꢂ
-ꢂ ꢂꢏꢌꢆꢂ+]ꢋꢅꢂꢄꢌꢆꢀꢂTꢂꢊꢄ+ꢅꢂ&+ &+ ꢅꢀ-ꢂ ꢂꢏꢌꢆꢂ+]ꢋꢅꢂꢏꢌꢐꢄꢂVꢂ Dꢂ VROLGꢂ PDWHULDOꢂ ZKLFKꢂ ZDVꢂUHFU\VWDOOL]HGꢂIURPꢂ LVRꢇ
ꢊꢆ+ꢅꢂꢈꢇ+ꢋꢅꢂꢐꢌꢁꢐꢂVꢂꢊꢆ+ꢅꢂꢀꢇ+ꢋꢅꢂꢐꢌꢀꢆꢂVꢂꢊꢆ+ꢅꢂ&+ 1ꢋꢌꢂ SURS\OꢂDOFRKROꢌꢂ<LHOGꢂꢁꢌꢆꢆꢐꢂJꢂꢊꢏꢃ=ꢋꢅꢂOLJKWꢂ\HOORZꢂ
)RXQGꢅꢂ=ꢓꢂ&ꢂꢀꢐꢌꢎꢐꢍꢂ+ꢂꢎꢌꢏꢆꢍꢂ1ꢂꢈꢄꢌꢐꢐꢌꢂ& + 1 ꢌꢂ&DOꢇ
FXODWHGꢅꢂ=ꢓꢂ&ꢂꢀꢑꢌꢁꢁꢍꢂ+ꢂꢎꢌꢎꢁꢍꢂ1ꢌꢄꢁꢌꢂ
FU\VWDOVꢅꢂPSꢂꢃꢎꢎ±ꢃꢎꢏ&ꢌꢂ,5ꢂVSHFWUXPꢅꢂ ꢅꢂFP ꢓꢂꢃꢎꢆꢁꢂ
ꢊ& 1ꢋꢍꢂꢃꢀꢀꢁꢅꢂꢃꢈꢎꢁꢂꢊS\UD]ROHꢋꢌꢂ +ꢂ105ꢂVSHFWUXPꢂ
ꢊDFHWRQHꢇG ꢋꢅꢂ ꢅꢂSSPꢓꢂꢃꢌꢄꢑꢂWꢂꢊꢎ+ꢅꢂ&+ &+ ꢅꢂ-ꢂ ꢂꢏꢌꢆꢂ+]ꢋꢅꢂ
ꢄꢌꢆꢀꢂTꢂꢊꢄ+ꢅꢂ&+ &+ ꢅꢀ-ꢂ ꢂꢏꢌꢆꢂ+]ꢋꢅꢂꢏꢌꢆꢃꢂVꢂꢊꢄ+ꢅꢂ+ ꢋꢅꢂ
ꢏꢌꢑꢃꢂVꢂꢊꢆ+ꢅꢂꢈꢇ+ꢋꢅꢂꢐꢌꢃꢎꢂVꢂꢊꢆ+ꢅꢂꢀꢇ+ꢋꢅꢂꢐꢌꢀꢃꢂVꢂꢊꢆ+ꢅꢂ&+ 1ꢋꢌꢂ
)RXQGꢅꢂ=ꢓꢂ&ꢂꢎꢏꢌꢀꢄꢍꢂ+ꢂꢎꢌꢁꢈꢍꢂ1ꢌꢑꢃꢌꢂ& + 1 ꢌꢂ&DOFXODWꢇ
HGꢅꢂ=ꢓꢂ&ꢂꢎꢏꢌꢄꢐꢍꢂ+ꢂꢎꢌꢆꢑꢍꢂ1ꢂꢆꢎꢌꢆꢈꢌ
ꢀꢁ(WK\OꢁꢆꢃꢇꢁGLPHWK\Oꢁꢀ+ꢁS\UD]ROHꢁꢂꢁFDUEDOGHꢁ
K\GH D]LQH ꢅ9EꢈꢂZDVꢂV\QWKHVL]HGꢂLQꢂDꢂVLPLODUꢂZD\ꢂ
IURPꢂꢁꢌꢃꢀꢆꢂJꢂꢊꢃꢂPPROꢋꢂRIꢂDOGHK\GHꢂ,,EꢂDQGꢂꢁꢌꢁꢎꢀꢂJꢂ
ꢊꢁꢌꢀꢂPPROꢋꢂRIꢂK\GUD]LQHꢂVXOIDWHꢌꢂ<LHOGꢂꢑꢀ=ꢅꢂFRORUOHVVꢂ
FU\VWDOVꢅꢂPSꢂꢃꢏꢀ±ꢃꢏꢎ&ꢂꢊIURPꢂEHQ]HQHꢋꢌꢂ,5ꢂVSHFWUXPꢅꢂ
ꢅꢂ FP ꢓꢂꢃꢎꢆꢁꢂ ꢊ& 1ꢋꢍꢂ ꢃꢀꢈꢁꢅꢂ ꢃꢄꢑꢁꢅꢂ ꢃꢈꢎꢁꢂꢊS\UD]ROHꢋꢌꢂꢂ
+ꢂ 105ꢂ VSHFWUXPꢂ ꢊDFHWRQHꢇG ꢋꢅꢂ ꢅꢂ SSPꢓꢂ ꢃꢌꢄꢏꢂ Wꢂ ꢊꢎ+ꢅꢂ
&+ &+ ꢅꢂ-ꢂ ꢂꢎꢌꢑꢂ+]ꢋꢅꢂꢆꢌꢄꢐꢂVꢂꢊꢎ+ꢅꢂꢈꢇ&+ ꢋꢅꢂꢆꢌꢎꢈꢂVꢂꢊꢎ+ꢅꢂ
ꢀꢇ&+ ꢋꢅꢂꢄꢌꢃꢑꢂTꢂꢊꢄ+ꢅꢂ&+ &+ ꢅꢂ-ꢂ ꢂꢎꢌꢑꢂ+]ꢋꢅꢂꢐꢌꢎꢑꢂVꢂꢂ
ꢊꢆ+ꢅꢂ&+ 1ꢋꢌꢂ)RXQGꢅꢂ=ꢓꢂ&ꢂꢎꢄꢌꢈꢑꢍꢂ+ꢂꢐꢌꢈꢐꢍꢂ1ꢂꢆꢏꢌꢏꢄꢌꢂ
& + 1 ꢌꢂ&DOFXODWHGꢅꢂ=ꢓꢂ&ꢌꢑꢏꢍꢂ+ꢂꢐꢌꢁꢀꢍꢂ1ꢂꢆꢏꢌꢑꢏꢌꢂ
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WKHVL]HGꢂ LQꢂ Dꢂ VLPLODUꢂ ZD\ꢂ IURPꢂ ꢁꢌꢎꢁꢐꢂ Jꢂ ꢊꢄꢂ PPROꢋꢂ RIꢂ
DOGHK\GHꢂ ,,Eꢂ DQGꢂ ꢁꢌꢆꢃꢎꢂ Jꢂ ꢊꢆꢂ PPROꢋꢂ RIꢂ SꢇSKHQ\OHQHꢇ
GLDPLQHꢌꢂ<LHOGꢂꢐꢎ=ꢅꢂPSꢂꢃꢏꢐ±ꢃꢏꢑ&ꢂꢊIURPꢂLꢇ3U2+±
+ 2ꢅꢂ ꢃꢓꢃꢋꢌꢂ ,5ꢂ VSHFWUXPꢅꢂ ꢅꢂFP ꢓꢂꢃꢎꢆꢁꢂꢊ& 1ꢋꢍꢂꢃꢀꢀꢁꢅꢂ
ꢃꢄꢄꢀꢅꢂꢃꢈꢀꢀꢂꢊS\UD]ROHꢋꢌꢂ +ꢂ105ꢂVSHFWUXPꢂꢊDFHWRQHꢇG ꢋꢅꢂ
ꢅꢂSSPꢓꢂꢃꢌꢈꢏꢂWꢂꢊꢎ+ꢅꢂ&+ &+ ꢅꢀ-ꢂ ꢂꢎꢌꢑꢂ+]ꢋꢅꢂꢆꢌꢄꢆꢂVꢂꢊꢎ+ꢅꢂ
ꢈꢇ&+ ꢋꢅꢂꢆꢌꢀꢐꢂVꢂꢊꢎ+ꢅꢂꢀꢇ&+ ꢋꢅꢂꢄꢌꢁꢑꢂTꢂꢊꢄ+ꢅꢂ&+ &+ ꢅꢀ-ꢂ ꢂ
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&ꢌꢃꢐꢍꢂ+ꢂꢏꢌꢀꢁꢍꢂ1ꢂꢆꢆꢌꢈꢆꢌꢂ
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ꢊꢆꢂPPROꢋꢂRIꢂFRPSRXQGꢂ,,DꢂDQGꢂꢁꢌꢁꢏꢐꢂJꢂꢊꢃꢂPPROꢋꢂRIꢂ
HWK\OHQHGLDPLQHꢂPRQRK\GUDWHꢂLQꢂꢃꢂPOꢂRIꢂEHQ]HQHꢂZDVꢂ
NHSWꢂ IRUꢂ ꢆꢄꢂ Kꢂ DWꢂ URRPꢂ WHPSHUDWXUHꢌꢂ 7KHꢂ VROYHQWꢂ ZDVꢂ
UHPRYHGꢅꢂDQGꢂWKHꢂVROLGꢂUHVLGXHꢂZDVꢂUHFU\VWDOOL]HGꢂIURPꢂ
KH[DQH±WROXHQHꢅꢂ ꢃꢓꢃꢌꢂ <LHOGꢂ ꢁꢌꢃꢎꢑꢂ Jꢂ ꢊꢎꢆ=ꢋꢅꢂ FRORUOHVVꢂ
FU\VWDOVꢅꢂPSꢂꢏꢐ±ꢏꢑ&ꢌꢂ,5ꢂVSHFWUXPꢅꢂ ꢅꢂFP ꢓꢂꢃꢎꢄꢀꢂ
ꢊ& 1ꢋꢍꢂ ꢃꢀꢀꢁꢅꢂ ꢃꢄꢄꢁꢅꢂ ꢃꢈꢐꢁꢂ ꢊS\UD]ROHꢋꢌꢂ +ꢂ 105ꢂ VSHFꢇ
WUXPꢂꢊDFHWRQHꢇG ꢋꢅꢂ ꢅꢂSSPꢓꢂꢃꢌꢄꢄꢂWꢂꢊꢎ+ꢅꢂ&+ &+ ꢅꢂ-ꢂ ꢂ
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ꢊꢆ+ꢅꢂ&+ 1ꢋꢌꢂ)RXQGꢅꢂ=ꢓꢂ&ꢌꢄꢑꢍꢂ+ꢂꢏꢌꢈꢏꢍꢂ1ꢂꢈꢃꢌꢁꢈꢌꢂ
& + 1 ꢌꢂ&DOFXODWHGꢅꢂ=ꢓꢂ&ꢂꢎꢃꢌꢏꢄꢍꢂ+ꢂꢏꢌꢄꢁꢍꢂ1ꢂꢈꢁꢌꢐꢎꢌ
1ꢁ1ꢀꢁ%LV>ꢅꢀꢁHWK\Oꢁꢀ+ꢁS\UD]ROꢁꢂꢁ\OꢈPHWK\OLGHQH@ꢁ
ELSKHQ\OꢁꢂꢃꢂꢄꢁGLDPLQH ꢅ9,,,Dꢈꢉꢂ$ꢂVROXWLRQꢂRIꢂꢁꢌꢆꢄꢐꢂJꢂ
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EHQ]LGLQHꢂ LQꢂ ꢃꢆꢂ POꢂ RIꢂ GLR[DQHꢂ ZDV ꢂ NHSWꢂ IRUꢂ ꢆꢄꢂ Kꢂ DWꢂ
URRPꢂWHPSHUDWXUHꢌꢂ7KHꢂPL[WXUHꢂZDVꢂSRXUHGꢂLQWRꢂꢐꢁꢂPOꢂ
RIꢂZDWHUꢅꢂDQGꢂWKHꢂSUHFLSLWDWHꢂZDVꢂILOWHUHGꢂRIIꢂDQGꢂGULHGꢌꢂ
<LHOGꢂ ꢁꢌꢈꢃꢀꢂ Jꢂ ꢊꢐꢁ=ꢋꢅꢂ PSꢂ ꢆꢃꢀ±ꢆꢃꢎ&ꢂ ꢊIURPꢂ KH[DQH±
WROXHQHꢅꢂꢃꢓꢃꢋꢌꢂ,5ꢂ VSHFWUXPꢅꢂ ꢅꢂ FP ꢓꢂ ꢃꢎꢆꢁꢂ ꢊ& 1ꢋꢍꢂꢃꢀꢐꢀꢂ
ꢊ& & ꢋꢍꢂꢃꢀꢄꢀꢅꢂꢃꢄꢄꢀꢅꢂꢃꢈꢐꢁꢂꢊS\UD]ROHꢋꢌꢂ +ꢂ105ꢂVSHFꢇ
WUXPꢂ ꢊDFHWRQHꢇG ꢋꢅꢂ ꢅꢂ SSPꢓꢂ ꢃꢌꢀꢃꢂ Wꢂ ꢊꢎ+ꢅꢂ &+ &+ ꢅꢀ -ꢂ ꢂꢂ
ꢏꢌꢆꢂ+]ꢋꢅꢂꢄꢌꢆꢐꢂTꢂꢊꢄ+ꢅꢂ&+ &+ ꢅꢀ-ꢂ ꢂꢏꢌꢆꢂ+]ꢋꢅꢂꢏꢌꢆꢐꢂGꢂꢊꢄ+ꢅꢂ
ꢈꢇ+ ꢅꢀ-ꢂ ꢂꢐꢌꢃꢂ+]ꢋꢅꢂꢏꢌꢏꢃꢂGꢂꢊꢄ+ꢅꢂꢆꢇ+ ꢅꢀ-ꢂ ꢂꢐꢌꢃꢂ+]ꢋꢅꢂ
ꢏꢌꢑꢄꢂVꢂꢊꢆ+ꢅꢂꢈꢇ+ꢋꢅꢂꢐꢌꢃꢑꢂꢊꢆ+ꢅꢂꢀꢇ+ꢋꢅꢂꢐꢌꢀꢀꢂVꢂꢊꢆ+ꢅꢂ&+ 1ꢋꢌꢂ
)RXQGꢅꢂ=ꢓꢂ&ꢂꢏꢆꢌꢑꢑꢍꢂ+ꢂꢎꢌꢆꢄꢍꢂ1ꢂꢆꢃꢌꢈꢏꢌꢂ& + 1 ꢌꢂ&DOꢇ
FXODWHGꢅꢂ=ꢓꢂ&ꢂꢏꢆꢌꢏꢁꢍꢂ+ꢂꢎꢌꢃꢁꢍꢂ1ꢂꢆꢃꢌꢆꢁꢌ
1ꢁ1ꢀꢁ%LV>ꢅꢀꢁHWK\OꢁꢆꢃꢇꢁGLPHWK\Oꢁꢀ+ꢁS\UD]ROꢁꢂꢁ\Oꢈꢁ
PHWK\OLGHQH@HWKDQHꢁꢀꢃꢋꢁGLDPLQH ꢅ9,EꢈꢂZDVꢂV\Qꢇ
WKHVL]HGꢂLQꢂDꢂVLPLODUꢂZD\ꢂIURPꢂꢁꢌꢄꢀꢎꢂJꢂꢊꢈꢂPPROꢋꢂRIꢂ
DOGHK\GHꢂ ,,Eꢂ DQGꢂ ꢁꢌꢃꢃꢏꢂ Jꢂ ꢊꢃꢌꢀꢂ PPROꢋꢂ RIꢂ HWK\OHQHGLꢇ
DPLQHꢂPRQRK\GUDWHꢌꢂ<LHOGꢂꢏꢏ=ꢅꢂPSꢂꢃꢁꢃꢌꢀ±ꢃꢁꢆꢌꢀ&ꢂ
ꢊIURPꢂ KH[DQH±WROXHQHꢅꢂ ꢈꢓꢃꢋꢌꢂ ,5ꢂ VSHFWUXPꢅꢂ ꢅꢂ FP ꢓꢂ
ꢃꢎꢄꢁꢂꢊ& 1ꢋꢍꢂꢃꢀꢀꢁꢅꢂꢃꢄꢄꢁꢅꢂꢃꢈꢎꢀꢂꢊS\UD]ROHꢋꢌꢂ +ꢂ105ꢂ
VSHFWUXPꢂꢊDFHWRQHꢇG ꢋꢅꢂ ꢅꢂSSPꢓꢂꢃꢌꢈꢆꢂWꢂꢊꢎ+ꢅꢂ&+ &+ ꢅꢀꢀ
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