WI: Philippe Auguste marries Richeza of Saxony not Ingeborg of Denmark

Richeza of Saxony is the mother of THomas of Perche, and sister of Otto the Holy Roman Emperor, if she marries Philippe Auguste, how would have history proceeded?
 
Philip II of France (b.1165: d.1223) m. Isabella of Hainault (b.1170: d.1190) (a), Richeza of Saxony (b.1172: d.1204) (b), Beatrice of Savoy (b.1205: d.1267) (c)

1a) Louis VIII of France (b.1187) m. Blanche of Castile (b.1188: d.1252) (a)

2a) Robert of France (b.1190: d.1190)

3a) Philippe of France (b.1190: d.1190)

4b) John of France (b.1193: d.1193)

5b) Marie of France (b.1194) m. Henry I, Duke of Brabant (b.1165: d.1235) (a)

1a) Elizabeth of Brabant (b.1212)

2a) Margaret of Brabant (b.1215)

3a) Miscarriage (c.1218)​

6b) Charles, Count of Artois (b.1197: d.1203)

7b) Isabelle of France (b.1201: d.1202)

8b) James, Count of Clermont-en-Beauvaisis (b.1203) m. Matilda II, Countess of Boulogne (b.1202: d.1259) (a)

1a) Alphonse, Count of Boulogne (b.1224)

2a) Alberic of Boulogne (b.1227: d.1227)

3a) Joan of Boulogne (b.1230)

4b) Blanche of Boulogne (b.1234)​
 
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