One column lists the 23 family members, mostly women and girls, who were taken by Islamic State militants last month when they stormed through a series of Yazidi villages in the north of Iraq on a rampage that left hundreds, if not thousands, dead.

The other column: the 17 relatives killed by the insurgents as they tried to escape to Mount Sinjar.

We are in a public school sheltering internally displaced people in the back streets of the northern Kurdish city of Dohuk to meet his cousin, a young woman who only the day before arrived at this shelter after escaping IS militants.

They held Kamal's cousin and 21 other young women captive for more than a month.

Zeitoun enters the classroom that is now home to more than a dozen people, mattresses and blankets piled almost to the ceiling, and sits beside me.

Upright, strong and articulate, the 23-year-old describes the moment that the militants captured her at a farmhouse she had fled to on the way to Mount Sinjar as IS fighters took over village after village. They separated their prisoners – men from women, women from girls.

"They killed the men, my father and seven others, right in front of my eyes and then took some other women into a school, threw fuel over them and planned to burn them," she says.

Across the room from us sit three of those women. One is weeping quietly – her daughter is still missing and she is moving between relief over Zeitoun's survival and grief that her daughter is not with her.

Zeitoun gestures to them. "They were the ones doused in petrol and Da'esh [IS] were going to set them alight. It is only that there was an air strike that made them run away, so they lived."

A woman enters the classroom to visit, her face erupting in relief and joy as she sees Zeitoun, one more who survived what everyone feared was certain death. If she kisses her once, she kisses her dozens of times, holding her face in disbelief and crying as she drinks in the idea that she is safe.

Zeitoun continues her story.

"They put us in three cars – 22 girls and women – and took us to the village of Baaj, then on to Mosul [a city that has been under the control of the Islamic State since June 10].

"Many things happened to us in the 11 days we were in Mosul," she says quietly. "You know why they had us – they were giving us to each other, passing us between themselves for sex."

Suddenly they were on the move again – Zeitoun was taken back to Baaj and her sister-in-law to Tal Afar. After two days she was moved again via minibus to another village called Tal Banat.

Along with the sexual violence there was also the beatings. Her wrists were tied together and she pulls down her bottom lip to reveal a deep cut that has yet to heal – the last time she was punched in the face for trying to resist an IS militant.

"Sometimes two men were hitting me at once and even though I was badly injured they would have sex with me every night, handing me from one man to the next.

"We were desperate to wash our faces, to clean the blood, but they would pour gasoline into the water and force us to use that," she says.

Everyone in the room is silent, frozen with the horror of her story.

"For one month and eight days I was in the hands of ISIL," she says. "I was their servant, I cooked for them, I did everything for them, but every day I tried to stop them hurting us."

On the day Zeitoun fled there was an air strike – she is not sure if it was US or Iraqi – and it gave her a moment to make her escape. "Before then we had decided to either kill ourselves or flee – these were our only options."

With a 13-year-old girl she managed to grab in the chaos after the air strike, Zeitoun walked for four days, with no food, water or shelter, hiding every time a car passed in case it was IS.

"We walked until we arrived at Sinjar Mountain," she says. "I saw some Yazidi fighters and we found the uncle of the girl I was with and left her with him."

An Amnesty International report released earlier this month echoes Zeitoun's testimony, as does a statement released by the United Nations Special Representative on sexual violence in conflict.

"There are allegations that many of the women and girls who have been abducted by IS fighters, notably girls in their teens and early 20s, have been subjected to rape or sexual abuse, forced to marry fighters, or sold into sexual slavery," the Amnesty report says.

Zainab Hawa Bangura, the UN Special Representative of the Secretary-General on Sexual Violence in Conflict, said: "Atrocious accounts on the abduction and detention of Yazidi, Christian, as well as Turkomen and Shabak women, girls and boys, and reports of savage rapes, are reaching us in an alarming manner."

Zeitoun and her family await news of their 21 female relatives still trapped in this cycle of violence.

Every day there is hope that -  as Zeitoun did - they will walk through the door of this overcrowded school now sheltering hundreds of Yazidi families.

But with each passing day, that hope dims.