the cold and a lack of supplies, so Gaozu left them behind and advanced to Pingcheng with only 40,000 men. Modu Chanyu saw his chance to turn the tide and immediately surrounded the city 400,000 cavalry, cutting the emperor off from the rest of his army. It's not clear why, but the Chanyu eventually withdrew some of his men. Sima Qian suggests his consort persuaded him to let the emperor escape. However a prolonged siege would have been impractical anyway since Xin's infantry never made it on time. Seeing the Chanyu's thinned lines, Gaozu sortied out and broke the siege. When Han reinforcements arrived, the Xiongnu withdrew. This came to be known as the Battle of Baideng. Gaozu's narrow escape from capture by the Xiongnu convinced him to make peace with his nomadic enemy. He sent a "princess" to the Chanyu (heqin, marriage alliance) and offered him silk, wine, and food stuffs. The Chanyu accepted the offer and restricted himself to minor raids throughout the duration of Gaozu's reign. The Han dynasty sent random unrelated commoner women falsely labeled as "princesses" and members of the Han imperial family multiple times when they were practicing heqin marriage alliances with the Xiongnu in order to avoid sending the emperor's daughters. After his Chinese campaign, Modu forced the Yuezhi and the Wusun to become vassals of the Xiongnu. In 195 BCE, Lu Wan King of Yan, fled to the Xiongnu after he was defeated by the Han general Zhou Bo. In 178 BCE, the Xiongnu overran the Yuezhi and Wusun in Gansu and the Tarim Basin. Modu died in 174 BCE and was succeeded by his son, Jiyu, who became Laoshang Chanyu. Marriage proposal to Empress Lü Zhi In 192 BC Empress Dowager Lü Zhi (widow of Emperor Gaozu of Han) received a marriage proposal from Modu, who wrote as follows in a letter meant to intimidate and mock her: I'm a lonesome ruler born in marshes and raised in plains populated by livestock. I've visited your border numerous times and wanted to tour China. Your Majesty is now alone and living in solitude. Since both of us are not happy and have nothing to entertain ourselves, I'm willing to use what I possess to exchange for what you lack. Lü Zhi was infuriated at the rude proposition, and in a heated court session, her generals advised her to rally an army and