How was the siege of Baden solved?

The siege of Deng Bai was an event in 200 BC (the seventh year of Emperor Gaozu) when Emperor Gaozu Liu Bang was besieged by Xiongnu in Deng Bai (now Mapu Mountain in the northeast of Datong City, Shanxi Province). In 20 1 year BC (the sixth year of Emperor Gaozu), Han Wangxin rebelled in Datong, colluded with Xiongnu and attempted to attack Taiyuan. Emperor gaozu Liu Bang personally led 320,000 troops to meet the Xiongnu, first winning in Tonggong (now Qinxian County, Shanxi Province) and then pursuing Loufan (now Ningwu, Shanxi Province). It was a cold winter and it snowed heavily. Liu Bang ignored Liu Jing's advice and stopped him. He rushed forward and chased Datong Pingcheng. The result was lured by the Huns. Liu bang and his vanguard troops were besieged in Dengbaishan, Pingcheng for 7 days and 7 nights, and completely cut off contact with the main force. Later, Liu Bang used Chen Ping's stratagem to bribe his wife, E Shi, to escape. [1] After the siege of Deng Baizhi, Liu Bang realized that it was not advisable to solve the dispute with Xiongnu only by force. Therefore, for a considerable period of time, adopting the policy of "pro-marriage" has become the main means to win over the Huns and maintain border peace.