What are the origins of these three idioms: "Retreat three homes", "unite with Lian Heng" and "make friends far away and attack near"?

1. During the Spring and Autumn Period, Jin Xiangong listened to rumors, killed Prince Shen Sheng, and sent someone to capture Shen Sheng's younger brother Zhong Er. After hearing the news, Zhong Er fled the State of Jin and lived in exile for more than ten years. After many hardships, Zhong Er came to the State of Chu. King Chu Cheng thought that Zhong Er would make great achievements in the future, so he greeted him with state gifts and regarded him as a distinguished guest. One day, the King of Chu gave a banquet in honor of Zhong Er. Two people drinking wine, chatting, the atmosphere is very harmonious. Suddenly, the king of Chu asked Zhong Er, "If one day you return to the State of Jin and become a monarch, how can you repay me?" Zhong Er thought for a moment and said, "Beautiful women are waiting for you, precious silk, and you have a lot of rare bird feathers, ivory leather, and even more in Chu. What rare items does Jin Wang have? " The king of Chu said, "You are too modest. Even so, you should show me something, right? " Zhong Er replied with a smile, "Thanks to you. If I can really return to China to be in power, I would like to get along well with your country. If one day, Jin Chu goes to war, I will definitely order the troops to retreat first (one house equals thirty miles). If I can't get your forgiveness, I will fight you again. "Four years later, Zhong Er really returned to the State of Jin and became a monarch. This is the famous Jin Wengong in history. The state of Jin became stronger and stronger under his rule. In 633 BC, the two armies of Chu and Jin fought. In order to fulfill his promise, Jin Wengong ordered the troops to retreat 90 miles and stay in Chengpu. When Chu Jun saw that 8 Jin J was retreating, he thought the other side was afraid and immediately pursued it. The Jin army took advantage of the weakness of the Chu army's pride in underestimating the enemy, concentrated its forces and defeated the Chu army greatly, and won the battle of Chengpu. 2. Foreign and military policies advocated and pursued by Lian Heng militarists during the Warring States Period. Su Qin once joined forces with "the whole world gathered in Zhao to attack Qin" ("The Warring States Policy, Qin Ce III"), lobbying the governors of the six countries to unite and explore the state of Qin in the west. Qin is in the west, the land of six countries, and the north and the south are connected, so it is called Lian. Lian Heng is in direct opposition to the integration policy. Zhang Yi once lobbied the six countries to let their colleagues work for the State of Qin. During the Warring States Period, Qi, Chu, Yan, Han, Zhao, Wei and Qin coexisted. In the mid-Warring States period, Qi and Qin were the most powerful countries, facing each other and fighting for allies in order to defeat each other. Not to be outdone, the other five countries sometimes confront and sometimes unite with Chyi Chin. Conflicts between major powers intensified and diplomatic activities became more frequent, which led to the struggle between Zonghe and Lian Heng. 3. At the beginning of the Spring and Autumn Period, Zhou's position was actually shelved, and the heroes rose together to compete for the Central Plains. In this chaotic situation, Zheng Zhuanggong skillfully used the strategy of "making friends far away and attacking near" and dared to win the hegemonic position at that time. At that time, Guo Song, Guo Wei and Zheng Guo, Zheng's close neighbors, had deep grievances and sharp contradictions, and Zheng was in danger of being attacked by the two countries at any time. Zheng took the initiative in diplomacy, forming alliances with Zhu, Lu and other countries, and soon signed an agreement with the powerful State of Qi in Shimen. In 7 19 BC, Chen and Cai jointly attacked Zheng, and Lu also sent troops to help and besieged Zhengdongmen for five days and five nights. Although he was not captured, Zheng felt that there was still a problem in the relationship between his country and Lu, so he tried every means to make up with Lu and deal with Song and Wei. In 7 17 BC, the state of Zheng attacked the state of Song in the name of helping the country to avenge itself. At the same time, he actively carried out diplomatic efforts with Shandong and sent envoys to Shandong to discuss the handover of Zheng's visit to Shandong. Sure enough, Lu Guohe solemnly restored the old friendship. Qi came forward to mediate the relationship between Zheng and Song. Show respect for Qi's opinion and make peace with Song for the time being. Qi thus deepened his feelings for Zheng. In 7 14 BC, Zheng Zhuanggong ordered an attack on the Song State on behalf of the Zhou Emperor on the grounds that the Song State did not worship the Zhou Emperor. The armies of Zheng, Qi and Lu soon occupied a large area of land in Song State. Song Weijun avoided the edge of the allied forces, took advantage of it and went straight for Zheng. Zheng Zhuanggong gave all the land occupied by Song to Qi and Lu, and quickly returned to Li, defeating the Song and Wei armies. Zheng pursued the victory and defeated Song State, and Wei State was forced to make peace. Zheng Zhuanggong's power has expanded and its hegemony has taken shape. Contact distant countries and attack neighboring countries. It was originally a diplomatic strategy adopted by Fan Ju towards Qin during the Warring States Period, and Qin used it to achieve the purpose of annexing six countries and establishing a unified dynasty. Later, it also refers to a means of dealing with others.